Bandwidth returns inf with discrete time transfer function

I am trying to find the 3dB frequency of discrete time transfer function using bandwidth but it returns inf. Here is the code:

alpha1=0.9;
ts = 0.1;
z = tf('z',ts);
H = ((1-alpha1)/2)*(1-z)/(1-alpha1*z);
fb = bandwidth(H,-3);

Am I doing anything conceptually wrong?

[Mathieu NOE]

Hi

read the doc

fb = bandwidth(sys) returns the bandwidth of the SISO dynamic system model sys. The bandwidth is the first frequency where the gain drops below 70.79% (-3 dB) of its DC value.

seems that this function cannot be used if you hae a high pass filter behaviour in your tf; because then the dc gain is 0 (-Inf in dB)

you have to write your own function for bandwith that overcomes this limitation

I recognize it's strange that this case is not dealed correctly in the native matlab function (shame on you TMW !)

all the best

[Shivanshu Sahoo]

Yeah I also thought the same but thought there must be something which I must be missing, so asked to confirm. Thanks for confirming.

[Mathieu NOE]

see the results of low pass vs high filters

bandwith works ok only for the low pass case

% high pass digital filter
alpha1=0.9;
ts = 0.1;
z = tf('z',ts);
H = ((1-alpha1)/2)*(1-z)/(1-alpha1*z);
figure(1),bode(H)
fb = bandwidth(H,-3);

% low pass analog filter
sys = tf(1,[1 1]);
fb = bandwidth(sys)
figure(2),bode(sys)

% high pass analog filter
sys = tf([1 0],[1 1]);
fb = bandwidth(sys)
figure(3),bode(sys)

[Shivanshu Sahoo]

Yes @Mathieu NOE you are correct. Bandwidth works only for low pass.

Answer 1

[Star Strider]

The -3 dB frequency is straightforward to calculate —

alpha1=0.9;
ts = 0.1;
z = tf('z',ts);
H = ((1-alpha1)/2)*(1-z)/(1-alpha1*z);
fb = bandwidth(H,-3)

fb = Inf

[mag,phase,wout] = bode(H);
mag = squeeze(mag);

wdB3 = interp1(mag2db(mag/max(mag)), wout, -3)

wdB3 = 1.0591

magdB3 = interp1(wout, mag2db(mag), wdB3)

magdB3 = -28.5751

phase = squeeze(phase);

figure
semilogx(wout, mag2db(mag))
hold on
plot(wdB3, magdB3, '+r', 'MarkerSize',10)
hold off
grid
xlim([min(wout) max(wout)])

.

[Shivanshu Sahoo]

What does wdB3 represent in our code?

[Star Strider]

It is the frequency corresponding to the -3 dB power.

.

[Shivanshu Sahoo]

Ok thank you so much

[Star Strider]

As always, my pleasure!

.