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spafe.utils.converters#

Description : Frequency converters implementation.
Copyright (c) 2019-2023 Ayoub Malek. This source code is licensed under the terms of the BSD 3-Clause License. For a copy, see <https://github.com/SuperKogito/spafe/blob/master/LICENSE>.

spafe.utils.converters.hz2erb(f: float, approach: Literal['Glasberg'] = 'Glasberg') → float[source]#

Convert Hz frequencies to Erb as referenced in [Glasberg].

Parameters

f (float) – input frequency [Hz].
approach (str) – conversion approach. (Default is “Glasberg”).

Returns

frequency in Erb [Erb].

Return type

(float)

Note

Glasberg (1990) :

\(fe = A . log_{10}(1 + f . 0.00437)\)
\(f = \frac{10^{\frac{fe}{A}} - 1}{0.00437}\)

where \(A = \frac{1000 . log_{e}(10)}{24.7 . 4.37}\)

! might raise: RuntimeWarning: invalid value encountered in log10

References

Glasberg(1,2): : Glasberg B. R., and Moore B. C. J. “Derivation of Auditory Filter Shapes from Notched-Noise Data.” Hearing Research. Vol. 47, Issues 1–2, 1990, pp. 103–138.

Examples

import matplotlib.pyplot as plt
from spafe.utils.converters import hz2erb

# generate freqs array -> convert freqs
hz_freqs = [freq for freq in range(0, 8000, 10)]
erb_freqs = [hz2erb(freq) for freq in hz_freqs]

# visualize conversion
plt.figure(figsize=(14,4))
plt.plot(hz_freqs, erb_freqs)
plt.xlabel("Frequency (Hz)")
plt.ylabel("Frequency (Erb)")
plt.title("Hertz to Erb scale frequency conversion")
plt.tight_layout()
plt.show()

spafe.utils.converters.erb2hz(fe: float, approach: Literal['Glasberg'] = 'Glasberg') → float[source]#

Convert Erb frequencies to Hz as referenced in [Glasberg].

Parameters

fe (float) – input frequency [Erb].
approach (str) – conversion approach. (Default is “Glasberg”).

Returns

frequency in Hz [Hz].

Return type

(float)

Note

Glasberg (1990) :

\(fe = A . log_{10}(1 + f . 0.00437)\)
\(f = \frac{10^{\frac{fe}{A}} - 1}{0.00437}\)

where \(A = \frac{1000 . log_{e}(10)}{24.7 . 4.37}\)

! might raise: RuntimeWarning: invalid value encountered in log10

Examples

import matplotlib.pyplot as plt
from spafe.utils.converters import erb2hz

# generate freqs array -> convert freqs
erb_freqs = [freq for freq in range(0, 35, 1)]
hz_freqs = [erb2hz(freq) for freq in erb_freqs]

# visualize conversion
plt.figure(figsize=(14,4))
plt.plot(erb_freqs, hz_freqs)
plt.xlabel("Frequency (Erb)")
plt.ylabel("Frequency (Hz)")
plt.title("Erb to Hertz frequency conversion")
plt.tight_layout()
plt.show()

spafe.utils.converters.hz2bark(f: float, approach: Literal['Wang', 'Tjomov', 'Schroeder', 'Terhardt', 'Zwicker', 'Traunmueller'] = 'Wang') → float[source]#

Convert Hz frequencies to Bark as mentioned in [Carter] and [Traunmueller].

Parameters

f (float) – input frequency [Hz].
approach (str) – conversion approach. (Default is “Wang”).

Returns

frequency in Bark [Bark].

Return type

(float)

Note

Tjomov (1971) :

\(fb = 6.7 . sinh^{-1}(\frac{f+20}{600})\)
\(f = 600 . sinh(\frac{fb}{6.7}) - 20\)

Schroeder (1977) :

\(fb = 7 . sinh^{-1}(\frac{f}{650})\)
\(f = 650 . sinh(\frac{fb}{7})\)

Terhardt (1979) :

\(fb = 13.3*tan^{-1}(\frac{0.75 . f}{1000})\)
\(f = (1000/0.75)*tan(\frac{fb}{13})\)

Zwicker & Terhardt (1980) :

\(fb = 8.7 + 14.2 . log10(\frac{f}{1000})\)
\(f = 10^{(\frac{fb-8.7}{14.2} + 3)}\)

Traunmueller (1983) :

\(fb = (\frac{26.81*f}{1+1960}) - 0.53\)
\(f = 1960 . (\frac{fb+0.53}{26.28-fb})\)

Wang, Sekey & Gersho (1992) :

\(fb = 6 . sinh^{-1}(\frac{f}{600})\)
\(f = 600 . sinh(\frac{fb}{6})\)

Examples

import matplotlib.pyplot as plt
from spafe.utils.converters import hz2bark

# generate freqs array -> convert freqs
hz_freqs = [freq for freq in range(0, 8000, 10)]
bark_freqs = [hz2bark(freq) for freq in hz_freqs]

# visualize conversion
plt.figure(figsize=(14,4))
plt.plot(hz_freqs, bark_freqs)
plt.xlabel("Frequency (Hz)")
plt.ylabel("Frequency (Bark)")
plt.title("Hertz to Bark scale frequency conversion")
plt.tight_layout()
plt.show()

spafe.utils.converters.bark2hz(fb: float, approach: Literal['Wang', 'Tjomov', 'Schroeder', 'Terhardt', 'Zwicker', 'Traunmueller'] = 'Wang') → float[source]#

Convert Bark frequencies to Hz as mentioned in [Carter] and [Traunmueller].

Parameters

fb (float) – input frequency [Bark].
approach (str) – conversion approach. (Default is “Wang”).

Returns

frequency in Hz [Hz].

Return type

(float)

Note

Tjomov (1971) :

\(fb = 6.7 . sinh^{-1}(\frac{f+20}{600})\)
\(f = 600 . sinh(\frac{fb}{6.7}) - 20\)

Schroeder (1977) :

\(fb = 7 . sinh^{-1}(\frac{f}{650})\)
\(f = 650 . sinh(\frac{fb}{7})\)

Terhardt (1979) :

\(fb = 13.3*tan^{-1}(\frac{0.75 . f}{1000})\)
\(f = (1000/0.75)*tan(\frac{fb}{13})\)

Zwicker & Terhardt (1980) :

\(fb = 8.7 + 14.2 . log10(\frac{f}{1000})\)
\(f = 10^{(\frac{fb-8.7}{14.2} + 3)}\)

! might raise RuntimeWarning: divide by zero encountered in log10

Traunmueller (1983) :

\(fb = (\frac{26.81*f}{1+1960}) - 0.53\)
\(f = 1960 . (\frac{fb+0.53}{26.28-fb})\)

Wang, Sekey & Gersho (1992) :

\(fb = 6 . sinh^{-1}(\frac{f}{600})\)
\(f = 600 . sinh(\frac{fb}{6})\)

References

Carter(1,2): Carter, P., “Sonification seminar – 10/9/03”, CCRMA.Stanford.edu., https://ccrma.stanford.edu/courses/120-fall-2003/lecture-5.html
Traunmueller(1,2): Traunmueller, H. (1990). Analytical expressions for the tonotopic sensory scale. The Journal of the Acoustical Society of America, 88(1), 97–100. doi:10.1121/1.399849

Examples

import matplotlib.pyplot as plt
from spafe.utils.converters import bark2hz

# generate freqs array -> convert freqs
bark_freqs = [freq for freq in range(0, 80, 5)]
hz_freqs = [bark2hz(freq) for freq in bark_freqs]

# visualize conversion
plt.figure(figsize=(14,4))
plt.plot(bark_freqs, hz_freqs)
plt.xlabel("Frequency (Bark)")
plt.ylabel("Frequency (Hz)")
plt.title("Bark to Hertz frequency conversion")
plt.tight_layout()
plt.show()

spafe.utils.converters.hz2mel(f: float, approach: Literal['Oshaghnessy', 'Lindsay'] = 'Oshaghnessy') → float[source]#

Convert a value in Hertz to Mels [Oshaghnessy], [Beranek] and [Lindsay].

Parameters

f (float) – input frequency [Hz].
approach (str) – conversion approach. (Default is “Oshaghnessy”).

Returns

frequency in Mel scale [Mel].

Return type

(float)

Note

Oshaghnessy (1987) :

\(fm = 2595 . log_{10}(1 + \frac{f}{700})\)
\(f = 700 . (10^{(\frac{fm}{2595} - 1)}\)

Beranek (1987) :

\(fm = 1127 . log_{e}(1 + \frac{f}{700})\)
\(f = 700 . exp(\frac{fm}{1127} - 1)\)

Both previous equations correspond to each other.

Lindsay (1977) :

\(fm = 2410 . log_{10}(1 + \frac{f}{625})\)
\(f = 625 . (10^{(\frac{fm}{2410} - 1)}\)

References

Oshaghnessy: : O’Shaghnessy, Douglas. Speech Communication: Human and Machine. Reading, MA: Addison-Wesley Publishing Company, 1987.
Beranek: : Beranek L.L. Acoustic Measurements, (1949) New York: Wiley.
Lindsay: : Lindsay, Peter H.; & Norman, Donald A. (1977). Human information processing: An introduction to psychology (2nd ed.). New York: Academic Press.

Examples

import matplotlib.pyplot as plt
from spafe.utils.converters import hz2mel

# generate freqs array -> convert freqs
hz_freqs = [freq for freq in range(0, 8000, 100)]
mel_freqs = [hz2mel(freq) for freq in hz_freqs]

# visualize conversion
plt.figure(figsize=(14,4))
plt.plot(hz_freqs, mel_freqs)
plt.xlabel("Frequency (Hz)")
plt.ylabel("Frequency (Mel)")
plt.title("Hertz to Mel frequency conversion")
plt.tight_layout()
plt.show()

spafe.utils.converters.mel2hz(fm: float, approach: Literal['Oshaghnessy', 'Lindsay'] = 'Oshaghnessy') → float[source]#

Convert a value in Mels to Hertz

Parameters

fm (float) – input frequency [Mel].
approach (str) – conversion approach. (Default is “Wang”).

Returns

frequency in Hz [Hz].

Return type

(float)

Examples

import matplotlib.pyplot as plt
from spafe.utils.converters import mel2hz

# generate freqs array -> convert freqs
mel_freqs = [freq for freq in range(0, 8000, 100)]
hz_freqs = [mel2hz(freq) for freq in mel_freqs]

# visualize conversion
plt.figure(figsize=(14,4))
plt.plot(mel_freqs, hz_freqs)
plt.xlabel("Frequency (Mel)")
plt.ylabel("Frequency (Hz)")
plt.title("Mel to Hertz frequency conversion")
plt.tight_layout()
plt.show()

spafe.utils.cepstral

spafe.utils.filters