zpk2tf and freqz functions implementation

[alykhaled]

I've created an implementation for zpk2tf function. The function is used to convert a zero-pole-gain representation of a filter to a transfer function representation where the return value is a array of numerator and denominator coefficients. The function is used in the design of digital filters.
The equivalent function in Matlab is zp2tf(z,p,k) and in Python is scipy.signal.zpk2tf(z,p,k).

I've also created an implementation for freqz function. The function is used to compute the frequency response of a digital filter. where it takes the numerator and denominator coefficients as input and returns the frequency response as an array of complex numbers.
The equivalent function in Matlab is freqz(b,a) and in Python is scipy.signal.freqz(b,a).

I want to create a PR but I don't know the right category for this functions, should it be in src/function/special or create a new category for it named signal or filter?

[josdejong]

Thanks Aly! That would be a useful addition. Good question what a suitable category would be. I think filter is a bit of an overloaded term, associated with filtering values from an Array, and special is mostly associated a function like erf. Maybe best to just follow the naming of Python here and name it signal?

One more question: what functions do we need to make this "feature complete"? Are there any related functions that we should implement too? (i.e. if you implement sin you should also implement cos and tan for example). I see the Matlab docs have an "See also" section, is there anything important there?

[alykhaled]

There are many function that we can implement to help in signal processing.
For example in the Linear Time Invariant Systems we can implement

• tf2zpk(b, a) : Return zero, pole, gain (z, p, k) representation from a numerator, denominator representation of a linear filter.
• tf2sos(b, a[, pairing, analog]) : Return second-order sections from transfer function representation
• tf2ss(num, den) : Transfer function to state-space representation.
• zpk2tf(z, p, k) : Return polynomial transfer function representation from zeros and poles
• zpk2sos(z, p, k[, pairing, analog]) : Return second-order sections from zeros, poles, and gain of a system
• zpk2ss(z, p, k) : Zero-pole-gain representation to state-space representation
• ss2tf(A, B, C, D[, input]) : State-space to transfer function.
• ss2zpk(A, B, C, D[, input]) : State-space representation to zero-pole-gain representation.
• sos2zpk(sos) : Return zeros, poles, and gain of a series of second-order sections
• sos2tf(sos) : Return a single transfer function from a series of second-order sections
• cont2discrete(system, dt[, method, alpha]) : Transform a continuous to a discrete state-space system.

Most of them are to change the representation from one type to another (zero, pole, gain, second-order sections, transfer function, state-space)

And in the filter design we can implement

• freqs(b, a[, worN, plot]) : Compute frequency response of analog filter.
• freqs_zpk(z, p, k[, worN]) : Compute frequency response of analog filter given zeros, poles and gain
• freqz(b[, a, worN, whole, plot, fs, ...]) : Compute the frequency response of a digital filter.
• freqz_zpk(z, p, k[, worN, whole, fs]) : Compute the frequency response of a digital filter in ZPK form.
• sosfreqz(sos[, worN, whole, fs]) : Compute the frequency response of a digital filter in SOS format.
• And many more ...

But for now I only implemented zpk2tf and freqz. My suggestion is to create a github project for the signal part with the remaining unimplemented functions so people would know.

Should I start a PR to implement these two functions ?

NB: ALL THE FUNCTIONS NAME AND DESCRIPTION IS FROM https://docs.scipy.org/doc/scipy/reference/signal.html

[josdejong]

Thanks for the clear overview!

But for now I only implemented zpk2tf and freqz. My suggestion is to create a github project for the signal part with the remaining unimplemented functions so people would know.

Ok sounds like a plan, let's start by implementing zpk2tf and freqz in mathjs itself. If the full set of functions is large (and not mainstream), we can indeed consider putting the functionality in a separate library, like other extensions: https://mathjs.org/download.html#extensions

Should I start a PR to implement these two functions ?

Yes please, thanks!

[josdejong]

Implemented via #2988 (not yet published)

[josdejong]

Published now in v11.9.0