Re: Plotting the frequency response of a filter in "real" Hz

[Sergei Steshenko]

>________________________________
> From: Guilherme Ritter <address@hidden>
>To: 
>Cc: address@hidden
>Sent: Friday, April 22, 2016 4:09 AM
>Subject: Re: Plotting the frequency response of a filter in "real" Hz
> 
>
>2016-04-21 20:09 GMT-03:00 Maynard Wright <address@hidden>:
>> On Wednesday, April 20, 2016 09:44:42 PM Guilherme Ritter wrote:
>>> Hi everyone.
>>>
>>> I've just started in filter design at college and I'm learning to use
>>> Octave for it. I want to see the frequency response of filters I design.
>>> I've managed to find code on the internet, but the output's x axis is in
>>> radian frequency. I'd like it to show "actual" Hz. For example, if the
>>> cutoff frequency is 5,5 kHz, I'd like for it to be represented in the
>>> plot's x axis at 5500 or 5,5.
>>>
>>> I've searched a lot but couldn't find anything, only some solutions that
>>> work in MatLab but not in Octave. At college, I'm using Octave 4.0.0,
>>> packages control 3.0.0 and signal 1.3.2, Windows 7 Enterprise x64. At home,
>>> all the versions are up to date, Xubuntu 14.04 x64.
>>>
>>> I've found the code here:
>>> https://ccrma.stanford.edu/~jos/fp/Example_LPF_Frequency_Response.html
>>>
>>> Can I use Octave's functions to get that plot the way I want it?
>>>
>>> Thanks in advance.
>>
>>
>> If you are plotting using
>>
>> plot(w,abs(H));
>>
>> as in the first example in the code you reference,  w is in radians per 
>> second.
>> You can create another vector that contains corresponding frequencies in Hz
>> and then use it in the plot:
>>
>> fHz = w / (2 * pi);
>> plot(fHz,abs(H));
>>
>> You will be using w in all the calculations and fHz just for the plotting.
>>
>> Maynard Wright
>>
>
>@ Mike Miller
>
>freqz (b, a, [], Fs);
>Mostly worked, but the scale of the x axis doesn't seem quite right.
>For example, I learned that the Butterworth filter, in the frequency
>response, have an y axis value of exactly 0,5 at the cutoff frequency.
>Using the code above, for cutoff = 10 kHz and sampling rate = 44,1
>kHz, the value at y = 0,5 is 10.382,8 Hz. Just to make sure we're on
>the same page, here's the code:
>
>% code BEGIN
>format long; pkg load signal;
>sampling_frequency = 44100;
>Nyquist_frequency = sampling_frequency / 2;
>cutoff_frequency = 10000;
>[filter_num, filter_den] = butter(10, cutoff_frequency / Nyquist_frequency);
>[frequency_H, frequency_w] = freqz(filter_num, filter_den, [],
>sampling_frequency);
>plot(frequency_w, abs(frequency_H));
>% code END
>
>--//--
>
>@ Sergei Steshenko
>
>error: freqresp: second argument 'w' must be a real-valued vector of 
>frequencies
>
>That's the last line in this code:
>
>% code BEGIN
>format long; pkg load signal;
>sampling_frequency = 44100;
>Nyquist_frequency = sampling_frequency / 2;
>cutoff_frequency = 10000;
>[filter_num, filter_den] = butter(10, cutoff_frequency / Nyquist_frequency);
>filter_s = tf(filter_num, filter_den);
>filter_z = c2d(filter_s, 1);
>number_of_points = 1000; % the bigger number of points, the better is
>resolution of the plot
>zfrequency_range = exp(pi * i * (0:number_of_points)
>/number_of_points); % from 0Hz to Nyquist frequency
>frequency_range = 0.5 * sampling_frequency * (0:number_of_points)
>/number_of_points); % from 0Hz to Nyquist frequency
>semilogx(frequency_range(2:end), 20 *
>log10(abs(filter_z(zfrequency_range(2:end))))); % 'filter_z' is your
>filter transfer function in 'z' domain
>% code END
>
>I used c2d as per the following link to transform the transfer
>function from S domain to Z domain. I don't know if it's the right
>way.
>http://octave.1599824.n4.nabble.com/Converting-from-S-to-Z-domain-td3317272.html
>
>And I added a missing open paren on the line that starts with
>"frequency_range = ..." where I imagined it was supposed to be. I
>tried with it in different positions but it didn't change the result.
>
>--//--
>
>@ Maynard Wright
>
>That just makes the x axis be between 0 and 0,5. Not what I'm looking
>for. I'm looking for Hz in the audio range.
>
>
>_______________________________________________
>Help-octave mailing list
>address@hidden
>https://lists.gnu.org/mailman/listinfo/help-octave
>
>

>

"
@ Sergei Steshenko

error: freqresp: second argument 'w' must be a real-valued vector of 
frequencies"

- I didn't use 'freqresp' function in my code. And I wrongly assumed you 
synthesized your filter in 'z' domain.

Type at Octave prompt

help butter

- the very first explanation is:

"
Generate a butterworth filter.
Default is a discrete space (Z) filter.

[b,a] = butter(n, Wc)
low pass filter with cutoff pi*Wc radians

".

Your filter transfer function to be used in 'semilogx' would be:

polyval(b,zfrequency_range(2:end)) ./ polyval(a,zfrequency_range(2:end))


--Sergei.