`scipy.signal` to‐do list

• Document filter representations (maybe in signal.rst? or else in individual function docstrings and link to each other) https://github.com/scipy/scipy/issues/3754
  • tf (added to tf2zpk Notes)
  • zpk
  • ss
  • sos
• zpk2sos:
  • Optimal pairing of poles and zeros to maximize SNR
    • Is this different for analog vs digital? https://github.com/scipy/scipy/pull/3717#issuecomment-46430634
  • Add order={'up', 'down'} argument to reverse section order
  • Add zeroflag={True, False} argument for pairing real zeros
  • Add scale={None, 'inf', 'two'} argument to output section scaling vector and optimization
    • sos = zpk2sos(z, p, k, scale=None) default, no g vector
    • sos, g = zpk2sos(z, p, k, scale='two'), returns a g vector too
    • https://github.com/scipy/scipy/pull/3717#issuecomment-45426872
  • Other examples:
    • sos = zpk2sos(z, p, k)
    • sos = zpk2sos(z, p, k, order='down')
    • sos, g = zpk2sos(z, p, k, order='up', scale='inf')
    • sos, g = zpk2sos(z, p, k, 'down', 'two', True)
  • Default: def zpk2sos(z, p, k, order='up', scale=None, zeroflag=False)
• sosfilt
  • Add a gain/scaling vector input? https://github.com/scipy/scipy/pull/3717#issuecomment-45427286
    • Last argument? def sosfilt(sos, x, axis=-1, zi=None, g=1)
      • k= or g=?
    • Or it could be a tuple as the first parameter y = sosfilt((sos, g), x) (goes with the "tuples are filter objects" theme)
  • could be smart about first-order sections and save a little time computing them https://github.com/Eric89GXL/scipy/pull/1
  • Option for Biquadratic vs. Direct-from II implementations, for numerical accuracy
• lfilter
  • actually lfilter could be smarter about exact zeros anywhere in a transfer function and save time by not computing them?
• filtfilt
  • Make it do forward-reverse sos filtering, or make a new function for this sosfiltfilt? → sosfiltfilt
• sos2tf
  • Should strip trailing zeros? https://github.com/scipy/scipy/pull/3717#issuecomment-45822044
• tf2zpk:
  • Add var={'s', 'z', 'z^-1'} argument for emulating both tf2zp and tf2zpk from matlab.
    • 's' and 'z' work as it currently does, like Matlab's tf2zp
    • 'z^-1' works like Matlab's tf2zpk
    • For common filters where M == N, there's no difference.
  • Same for tf2ss, tf2sos, etc.
• zpk2ss
  • Add form={'controllable', 'observable', 'cascade', 'jordan', ...} parameter
  • Uses tf2ss(*zpk2tf, and tf is lossy numerically, so if other forms allow better numerical behavior, convert to those directly, not through tf. https://github.com/scipy/scipy/issues/5912
  • zpk2ss uses a zeros-along-the-diagonal form by default and tf2ss uses controllable canonical form by default? since these are the most similar to the source representation?
• cplxpair
  • Print the pair that caused the exception
  • Accept N-D array inputs
• freqz and freqs
  • needs to support some filter representations other than lossy tf https://github.com/scipy/scipy/issues/3259
• Optimum L filters?
  • Make a filter design function?
    • https://gist.github.com/endolith/c80f9e6bf3b407c2f567
  • Add to SciPy
• Bessel filters
  • All 3 normalizations
  • Higher orders than 25
  • https://gist.github.com/endolith/3f74c4ec9ea623812cca
  • https://github.com/scipy/scipy/issues/3763
  • Modify besselap
  • Modify bessel https://github.com/scipy/scipy/pull/5279
  • Add example of time-domain filtering of digital signal?
• _zpklp2hp, etc
  • Make public versions of these functions, or somehow combine with existing ones
  • https://github.com/scipy/scipy/pull/3085 (used private functions for now)
  • https://github.com/scipy/scipy/issues/3259 (maybe needs new API)
• convolve and correlate
  • Speed up by calling fftconvolve
    • new parameter method={'fft', 'direct', 'auto'}
    • https://github.com/scipy/scipy/issues/2651
  • axis= parameter (requires C changes? or could be hacked in as a for loop)
• Window functions:
  • chebwin
    • Change to frequency domain normalization so center bump is 1 instead of spikes https://github.com/scipy/scipy/issues/2221
    • use DCT to be faster?
  • slepian
    • Fix normalization https://github.com/scipy/scipy/issues/2221
    • Confirm correctness
  • exact_blackman http://zone.ni.com/reference/en-XX/help/372058H-01/rfsapropref/pnirfsa_spectrum.fftwindowtype/
  • general_blackman http://en.wikipedia.org/wiki/Window_function#Blackman_windows
    • or add a a=0.16 parameter to the existing blackman
  • blackmanharris
    • add 7-term version or n-term? http://zone.ni.com/reference/en-XX/help/372058H-01/rfsapropref/pnirfsa_spectrum.fftwindowtype/
• buttord etc
  • Double check all 16 cases to see that frequency tightness is on correct side https://github.com/scipy/scipy/issues/3219#issuecomment-33168829
• dct
  • implement all 8 types and therefore odd-order DFT sizes? http://en.wikipedia.org/wiki/Discrete_cosine_transform#DCT_V-VIII
    • This could be used in chebwin, for instance
  • handle integer input better https://github.com/scipy/scipy/pull/2776
    • Needs unit tests
• biquad cookbook functions
  • Add all the types
  • https://gist.github.com/endolith/5455375
  • Combine them where possible (btype={'low', 'high'}, etc)
• lti
  • Printable representation of transfer functions?
  • Discrete-time systems (https://github.com/scipy/scipy/issues/2912, https://github.com/scipy/scipy/pull/4881)
• decimate
  • use sosfiltfilt instead of lfilter (partly implemented by parameter zero_phase)
  • Polyphase FIR implementation to save processing time