How to filter a signal with a transfer function?

Hi!

I have a discrete signal (a vector with many values) I want to filter using a low pass filter but I only have the tranfer function in the form. How can I do this since the common filter functions dont use transforms?

Answer 1

[Star Strider]

The easiest approach is to first let the Control System Toolbox solve it, then realise it as a discrete filter using the numerator and denominator vectors —

z = tf('z');
H = (1-z^-6)^2 / (1-z^-1)^2

H =
 
   z^14 - 2 z^8 + z^2
  --------------------
  z^14 - 2 z^13 + z^12
 
Sample time: unspecified
Discrete-time transfer function.

Num = H.Numerator

Num = 1×1 cell array
    {[1 0 0 0 0 0 -2 0 0 0 0 0 1 0 0]}

Den = H.Denominator

Den = 1×1 cell array
    {[1 -2 1 0 0 0 0 0 0 0 0 0 0 0 0]}

figure
freqz(Num{:}, Den{:}, 2^16)

Use ‘Num{:}’ and ‘Den{:}’ with filtfilt to filter the signal.

Remember that it will be necessary to define a sampling interval, ‘Ts’ where ‘Ts=1/Fs’ where ‘Fs’ is the sampling frequency.

.

[Ana Gabriela Guedes]

Thank you! Where sould I insert de sampling interval?

I'm getting the error that filtfilt arguments should me double matrices and I only have row vectors

[Star Strider]

No, use the filtfilt function to filter ‘x’.

Assuming that the sampling interval or sampling frequency is defined in the first tf call:

Fs = 1000;                                          % Define Sampling Frequency
Ts = 1/Fs;
z = tf('z',Ts);
H = (1-z^-6)^2 / (1-z^-1)^2

H =
 
   z^14 - 2 z^8 + z^2
  --------------------
  z^14 - 2 z^13 + z^12
 
Sample time: 0.001 seconds
Discrete-time transfer function.

Num = H.Numerator

Num = 1×1 cell array
    {[1 0 0 0 0 0 -2 0 0 0 0 0 1 0 0]}

Den = H.Denominator

Den = 1×1 cell array
    {[1 -2 1 0 0 0 0 0 0 0 0 0 0 0 0]}

figure
freqz(Num{:}, Den{:}, 2^16, Fs)

x = [-233....-667]
x_filtered = filtfilt(Num{:}, Den{:}, x)

and go from there.

.