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Merge branch 'TheAlgorithms:master' into Euler-P78
2 parents f540cc6 + 31061aa commit 7287753

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‎DIRECTORY.md

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* [Newton Raphson](https://github.com/TheAlgorithms/Python/blob/master/arithmetic_analysis/newton_raphson.py)
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* [Secant Method](https://github.com/TheAlgorithms/Python/blob/master/arithmetic_analysis/secant_method.py)
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## Audio Filters
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* [Butterworth Filter](https://github.com/TheAlgorithms/Python/blob/master/audio_filters/butterworth_filter.py)
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* [Iir Filter](https://github.com/TheAlgorithms/Python/blob/master/audio_filters/iir_filter.py)
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* [Show Response](https://github.com/TheAlgorithms/Python/blob/master/audio_filters/show_response.py)
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## Backtracking
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* [All Combinations](https://github.com/TheAlgorithms/Python/blob/master/backtracking/all_combinations.py)
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* [All Permutations](https://github.com/TheAlgorithms/Python/blob/master/backtracking/all_permutations.py)
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## Cellular Automata
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* [Conways Game Of Life](https://github.com/TheAlgorithms/Python/blob/master/cellular_automata/conways_game_of_life.py)
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* [Game Of Life](https://github.com/TheAlgorithms/Python/blob/master/cellular_automata/game_of_life.py)
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* [Nagel Schrekenberg](https://github.com/TheAlgorithms/Python/blob/master/cellular_automata/nagel_schrekenberg.py)
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* [One Dimensional](https://github.com/TheAlgorithms/Python/blob/master/cellular_automata/one_dimensional.py)
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## Ciphers
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* [Base64 Encoding](https://github.com/TheAlgorithms/Python/blob/master/ciphers/base64_encoding.py)
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* [Base85](https://github.com/TheAlgorithms/Python/blob/master/ciphers/base85.py)
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* [Beaufort Cipher](https://github.com/TheAlgorithms/Python/blob/master/ciphers/beaufort_cipher.py)
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* [Bifid](https://github.com/TheAlgorithms/Python/blob/master/ciphers/bifid.py)
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* [Brute Force Caesar Cipher](https://github.com/TheAlgorithms/Python/blob/master/ciphers/brute_force_caesar_cipher.py)
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* [Caesar Cipher](https://github.com/TheAlgorithms/Python/blob/master/ciphers/caesar_cipher.py)
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* [Cryptomath Module](https://github.com/TheAlgorithms/Python/blob/master/ciphers/cryptomath_module.py)
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## Conversions
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* [Binary To Decimal](https://github.com/TheAlgorithms/Python/blob/master/conversions/binary_to_decimal.py)
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* [Binary To Hexadecimal](https://github.com/TheAlgorithms/Python/blob/master/conversions/binary_to_hexadecimal.py)
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* [Binary To Octal](https://github.com/TheAlgorithms/Python/blob/master/conversions/binary_to_octal.py)
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* [Decimal To Any](https://github.com/TheAlgorithms/Python/blob/master/conversions/decimal_to_any.py)
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* [Decimal To Binary](https://github.com/TheAlgorithms/Python/blob/master/conversions/decimal_to_binary.py)
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* [Rgb Hsv Conversion](https://github.com/TheAlgorithms/Python/blob/master/conversions/rgb_hsv_conversion.py)
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* [Roman Numerals](https://github.com/TheAlgorithms/Python/blob/master/conversions/roman_numerals.py)
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* [Temperature Conversions](https://github.com/TheAlgorithms/Python/blob/master/conversions/temperature_conversions.py)
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* [Volume Conversions](https://github.com/TheAlgorithms/Python/blob/master/conversions/volume_conversions.py)
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* [Weight Conversion](https://github.com/TheAlgorithms/Python/blob/master/conversions/weight_conversion.py)
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## Data Structures
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* Tests
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* [Test Send File](https://github.com/TheAlgorithms/Python/blob/master/file_transfer/tests/test_send_file.py)
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## Financial
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* [Interest](https://github.com/TheAlgorithms/Python/blob/master/financial/interest.py)
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## Fractals
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* [Julia Sets](https://github.com/TheAlgorithms/Python/blob/master/fractals/julia_sets.py)
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* [Koch Snowflake](https://github.com/TheAlgorithms/Python/blob/master/fractals/koch_snowflake.py)
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* [Multi Heuristic Astar](https://github.com/TheAlgorithms/Python/blob/master/graphs/multi_heuristic_astar.py)
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* [Page Rank](https://github.com/TheAlgorithms/Python/blob/master/graphs/page_rank.py)
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* [Prim](https://github.com/TheAlgorithms/Python/blob/master/graphs/prim.py)
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* [Random Graph Generator](https://github.com/TheAlgorithms/Python/blob/master/graphs/random_graph_generator.py)
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* [Scc Kosaraju](https://github.com/TheAlgorithms/Python/blob/master/graphs/scc_kosaraju.py)
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* [Strongly Connected Components](https://github.com/TheAlgorithms/Python/blob/master/graphs/strongly_connected_components.py)
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* [Tarjans Scc](https://github.com/TheAlgorithms/Python/blob/master/graphs/tarjans_scc.py)
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* [Capitalize](https://github.com/TheAlgorithms/Python/blob/master/strings/capitalize.py)
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* [Check Anagrams](https://github.com/TheAlgorithms/Python/blob/master/strings/check_anagrams.py)
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* [Check Pangram](https://github.com/TheAlgorithms/Python/blob/master/strings/check_pangram.py)
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* [Credit Card Validator](https://github.com/TheAlgorithms/Python/blob/master/strings/credit_card_validator.py)
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* [Detecting English Programmatically](https://github.com/TheAlgorithms/Python/blob/master/strings/detecting_english_programmatically.py)
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* [Frequency Finder](https://github.com/TheAlgorithms/Python/blob/master/strings/frequency_finder.py)
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* [Indian Phone Validator](https://github.com/TheAlgorithms/Python/blob/master/strings/indian_phone_validator.py)
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* [Rabin Karp](https://github.com/TheAlgorithms/Python/blob/master/strings/rabin_karp.py)
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* [Remove Duplicate](https://github.com/TheAlgorithms/Python/blob/master/strings/remove_duplicate.py)
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* [Reverse Letters](https://github.com/TheAlgorithms/Python/blob/master/strings/reverse_letters.py)
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* [Reverse Long Words](https://github.com/TheAlgorithms/Python/blob/master/strings/reverse_long_words.py)
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* [Reverse Words](https://github.com/TheAlgorithms/Python/blob/master/strings/reverse_words.py)
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* [Split](https://github.com/TheAlgorithms/Python/blob/master/strings/split.py)
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* [Upper](https://github.com/TheAlgorithms/Python/blob/master/strings/upper.py)
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* [Fetch Jobs](https://github.com/TheAlgorithms/Python/blob/master/web_programming/fetch_jobs.py)
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* [Get Imdb Top 250 Movies Csv](https://github.com/TheAlgorithms/Python/blob/master/web_programming/get_imdb_top_250_movies_csv.py)
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* [Get Imdbtop](https://github.com/TheAlgorithms/Python/blob/master/web_programming/get_imdbtop.py)
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* [Get Top Hn Posts](https://github.com/TheAlgorithms/Python/blob/master/web_programming/get_top_hn_posts.py)
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* [Get User Tweets](https://github.com/TheAlgorithms/Python/blob/master/web_programming/get_user_tweets.py)
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* [Giphy](https://github.com/TheAlgorithms/Python/blob/master/web_programming/giphy.py)
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* [Instagram Crawler](https://github.com/TheAlgorithms/Python/blob/master/web_programming/instagram_crawler.py)
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* [Instagram Pic](https://github.com/TheAlgorithms/Python/blob/master/web_programming/instagram_pic.py)

‎audio_filters/__init__.py

Whitespace-only changes.

‎audio_filters/butterworth_filter.py

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from math import cos, sin, sqrt, tau
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from audio_filters.iir_filter import IIRFilter
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"""
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Create 2nd-order IIR filters with Butterworth design.
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Code based on https://webaudio.github.io/Audio-EQ-Cookbook/audio-eq-cookbook.html
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Alternatively you can use scipy.signal.butter, which should yield the same results.
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"""
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def make_lowpass(
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frequency: int, samplerate: int, q_factor: float = 1 / sqrt(2)
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) -> IIRFilter:
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"""
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Creates a low-pass filter
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>>> filter = make_lowpass(1000, 48000)
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>>> filter.a_coeffs + filter.b_coeffs # doctest: +NORMALIZE_WHITESPACE
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[1.0922959556412573, -1.9828897227476208, 0.9077040443587427, 0.004277569313094809,
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0.008555138626189618, 0.004277569313094809]
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"""
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w0 = tau * frequency / samplerate
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_sin = sin(w0)
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_cos = cos(w0)
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alpha = _sin / (2 * q_factor)
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b0 = (1 - _cos) / 2
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b1 = 1 - _cos
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a0 = 1 + alpha
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a1 = -2 * _cos
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a2 = 1 - alpha
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filt = IIRFilter(2)
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filt.set_coefficients([a0, a1, a2], [b0, b1, b0])
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return filt
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def make_highpass(
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frequency: int, samplerate: int, q_factor: float = 1 / sqrt(2)
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) -> IIRFilter:
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"""
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Creates a high-pass filter
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>>> filter = make_highpass(1000, 48000)
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>>> filter.a_coeffs + filter.b_coeffs # doctest: +NORMALIZE_WHITESPACE
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[1.0922959556412573, -1.9828897227476208, 0.9077040443587427, 0.9957224306869052,
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-1.9914448613738105, 0.9957224306869052]
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"""
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w0 = tau * frequency / samplerate
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_sin = sin(w0)
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_cos = cos(w0)
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alpha = _sin / (2 * q_factor)
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b0 = (1 + _cos) / 2
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b1 = -1 - _cos
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a0 = 1 + alpha
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a1 = -2 * _cos
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a2 = 1 - alpha
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filt = IIRFilter(2)
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filt.set_coefficients([a0, a1, a2], [b0, b1, b0])
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return filt
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def make_bandpass(
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frequency: int, samplerate: int, q_factor: float = 1 / sqrt(2)
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) -> IIRFilter:
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"""
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Creates a band-pass filter
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>>> filter = make_bandpass(1000, 48000)
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>>> filter.a_coeffs + filter.b_coeffs # doctest: +NORMALIZE_WHITESPACE
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[1.0922959556412573, -1.9828897227476208, 0.9077040443587427, 0.06526309611002579,
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0, -0.06526309611002579]
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"""
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w0 = tau * frequency / samplerate
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_sin = sin(w0)
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_cos = cos(w0)
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alpha = _sin / (2 * q_factor)
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b0 = _sin / 2
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b1 = 0
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b2 = -b0
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a0 = 1 + alpha
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a1 = -2 * _cos
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a2 = 1 - alpha
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filt = IIRFilter(2)
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filt.set_coefficients([a0, a1, a2], [b0, b1, b2])
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return filt
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def make_allpass(
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frequency: int, samplerate: int, q_factor: float = 1 / sqrt(2)
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) -> IIRFilter:
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"""
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Creates an all-pass filter
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>>> filter = make_allpass(1000, 48000)
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>>> filter.a_coeffs + filter.b_coeffs # doctest: +NORMALIZE_WHITESPACE
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[1.0922959556412573, -1.9828897227476208, 0.9077040443587427, 0.9077040443587427,
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-1.9828897227476208, 1.0922959556412573]
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"""
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w0 = tau * frequency / samplerate
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_sin = sin(w0)
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_cos = cos(w0)
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alpha = _sin / (2 * q_factor)
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b0 = 1 - alpha
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b1 = -2 * _cos
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b2 = 1 + alpha
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filt = IIRFilter(2)
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filt.set_coefficients([b2, b1, b0], [b0, b1, b2])
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return filt
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def make_peak(
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frequency: int, samplerate: int, gain_db: float, q_factor: float = 1 / sqrt(2)
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) -> IIRFilter:
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"""
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Creates a peak filter
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>>> filter = make_peak(1000, 48000, 6)
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>>> filter.a_coeffs + filter.b_coeffs # doctest: +NORMALIZE_WHITESPACE
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[1.0653405327119334, -1.9828897227476208, 0.9346594672880666, 1.1303715025601122,
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-1.9828897227476208, 0.8696284974398878]
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"""
134+
w0 = tau * frequency / samplerate
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_sin = sin(w0)
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_cos = cos(w0)
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alpha = _sin / (2 * q_factor)
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big_a = 10 ** (gain_db / 40)
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b0 = 1 + alpha * big_a
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b1 = -2 * _cos
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b2 = 1 - alpha * big_a
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a0 = 1 + alpha / big_a
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a1 = -2 * _cos
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a2 = 1 - alpha / big_a
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filt = IIRFilter(2)
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filt.set_coefficients([a0, a1, a2], [b0, b1, b2])
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return filt
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def make_lowshelf(
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frequency: int, samplerate: int, gain_db: float, q_factor: float = 1 / sqrt(2)
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) -> IIRFilter:
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"""
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Creates a low-shelf filter
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>>> filter = make_lowshelf(1000, 48000, 6)
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>>> filter.a_coeffs + filter.b_coeffs # doctest: +NORMALIZE_WHITESPACE
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[3.0409336710888786, -5.608870992220748, 2.602157875636628, 3.139954022810743,
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-5.591841778072785, 2.5201667380627257]
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"""
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w0 = tau * frequency / samplerate
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_sin = sin(w0)
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_cos = cos(w0)
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alpha = _sin / (2 * q_factor)
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big_a = 10 ** (gain_db / 40)
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pmc = (big_a + 1) - (big_a - 1) * _cos
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ppmc = (big_a + 1) + (big_a - 1) * _cos
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mpc = (big_a - 1) - (big_a + 1) * _cos
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pmpc = (big_a - 1) + (big_a + 1) * _cos
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aa2 = 2 * sqrt(big_a) * alpha
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b0 = big_a * (pmc + aa2)
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b1 = 2 * big_a * mpc
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b2 = big_a * (pmc - aa2)
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a0 = ppmc + aa2
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a1 = -2 * pmpc
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a2 = ppmc - aa2
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filt = IIRFilter(2)
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filt.set_coefficients([a0, a1, a2], [b0, b1, b2])
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return filt
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def make_highshelf(
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frequency: int, samplerate: int, gain_db: float, q_factor: float = 1 / sqrt(2)
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) -> IIRFilter:
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"""
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Creates a high-shelf filter
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>>> filter = make_highshelf(1000, 48000, 6)
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>>> filter.a_coeffs + filter.b_coeffs # doctest: +NORMALIZE_WHITESPACE
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[2.2229172136088806, -3.9587208137297303, 1.7841414181566304, 4.295432981120543,
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-7.922740859457287, 3.6756456963725253]
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"""
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w0 = tau * frequency / samplerate
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_sin = sin(w0)
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_cos = cos(w0)
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alpha = _sin / (2 * q_factor)
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big_a = 10 ** (gain_db / 40)
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pmc = (big_a + 1) - (big_a - 1) * _cos
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ppmc = (big_a + 1) + (big_a - 1) * _cos
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mpc = (big_a - 1) - (big_a + 1) * _cos
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pmpc = (big_a - 1) + (big_a + 1) * _cos
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aa2 = 2 * sqrt(big_a) * alpha
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b0 = big_a * (ppmc + aa2)
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b1 = -2 * big_a * pmpc
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b2 = big_a * (ppmc - aa2)
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a0 = pmc + aa2
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a1 = 2 * mpc
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a2 = pmc - aa2
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filt = IIRFilter(2)
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filt.set_coefficients([a0, a1, a2], [b0, b1, b2])
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return filt

‎audio_filters/iir_filter.py

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from __future__ import annotations
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class IIRFilter:
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r"""
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N-Order IIR filter
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Assumes working with float samples normalized on [-1, 1]
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---
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Implementation details:
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Based on the 2nd-order function from
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https://en.wikipedia.org/wiki/Digital_biquad_filter,
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this generalized N-order function was made.
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Using the following transfer function
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H(z)=\frac{b_{0}+b_{1}z^{-1}+b_{2}z^{-2}+...+b_{k}z^{-k}}{a_{0}+a_{1}z^{-1}+a_{2}z^{-2}+...+a_{k}z^{-k}}
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we can rewrite this to
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y[n]={\frac{1}{a_{0}}}\left(\left(b_{0}x[n]+b_{1}x[n-1]+b_{2}x[n-2]+...+b_{k}x[n-k]\right)-\left(a_{1}y[n-1]+a_{2}y[n-2]+...+a_{k}y[n-k]\right)\right)
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"""
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def __init__(self, order: int) -> None:
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self.order = order
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# a_{0} ... a_{k}
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self.a_coeffs = [1.0] + [0.0] * order
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# b_{0} ... b_{k}
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self.b_coeffs = [1.0] + [0.0] * order
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# x[n-1] ... x[n-k]
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self.input_history = [0.0] * self.order
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# y[n-1] ... y[n-k]
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self.output_history = [0.0] * self.order
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def set_coefficients(self, a_coeffs: list[float], b_coeffs: list[float]) -> None:
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"""
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Set the coefficients for the IIR filter. These should both be of size order + 1.
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a_0 may be left out, and it will use 1.0 as default value.
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This method works well with scipy's filter design functions
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>>> # Make a 2nd-order 1000Hz butterworth lowpass filter
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>>> import scipy.signal
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>>> b_coeffs, a_coeffs = scipy.signal.butter(2, 1000,
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... btype='lowpass',
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... fs=48000)
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>>> filt = IIRFilter(2)
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>>> filt.set_coefficients(a_coeffs, b_coeffs)
48+
"""
49+
if len(a_coeffs) < self.order:
50+
a_coeffs = [1.0] + a_coeffs
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if len(a_coeffs) != self.order + 1:
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raise ValueError(
54+
f"Expected a_coeffs to have {self.order + 1} elements for {self.order}"
55+
f"-order filter, got {len(a_coeffs)}"
56+
)
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if len(b_coeffs) != self.order + 1:
59+
raise ValueError(
60+
f"Expected b_coeffs to have {self.order + 1} elements for {self.order}"
61+
f"-order filter, got {len(a_coeffs)}"
62+
)
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self.a_coeffs = a_coeffs
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self.b_coeffs = b_coeffs
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def process(self, sample: float) -> float:
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"""
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Calculate y[n]
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>>> filt = IIRFilter(2)
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>>> filt.process(0)
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0.0
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"""
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result = 0.0
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# Start at index 1 and do index 0 at the end.
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for i in range(1, self.order + 1):
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result += (
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self.b_coeffs[i] * self.input_history[i - 1]
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- self.a_coeffs[i] * self.output_history[i - 1]
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)
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result = (result + self.b_coeffs[0] * sample) / self.a_coeffs[0]
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self.input_history[1:] = self.input_history[:-1]
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self.output_history[1:] = self.output_history[:-1]
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self.input_history[0] = sample
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self.output_history[0] = result
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return result

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