question on Allpass filter

[gadagkar.rohit]

Hello,

I am designing an all pass filter which is a part of a reverberation generator for audio inputs. I am implementing it in verilog.

The difference equation that i am using is

y = x(n-N) - g*x + g*y(n-N);
g - gain, N - filter order
the transfer function is H(z) = [-g + Z^(-N)]/[1 - g*Z^(-N)]

With g = 0.2, when I give a sine input at 5 KHz at -40db, the output is +5db. so the gain is 45db.

I am really confused with the overall result. how exactly is the value of g affecting the gain.

Please let me know if I ve gone wrong at any step or my understanding. Please help me with this.

 

[FvM]

Where did you get the difference equation? It doesn't look like a valid all pass at first sight. Compare https://en.wikipedia.org/wiki/All-pass_filter

 

[gadagkar.rohit]

when i plot the frequency response using matlab with filter coefficients b = [-0.2 0 0 0 1] and a= [1 0 0 0 -0.2] i got a flat spectrum (here N = 3, g = 0.2). or for that matter with any value of N, i got a flat spectrum.
i used freqz(b,a).

---------- Post added at 09:47 ---------- Previous post was at 09:41 ----------

initially i was given this equation to use,
y = g*y(n-N) - x + (1+g)*x(n-N);
but that equation didnt give a flat spectrum. does this look like one?

 

[RaulPinheiro]

For different frequencies, you get different gains and different phases (lags). g is a filter parameter, which is not directly related to the filter overall gain on a given frequency. U can plot |H(jw,g)| for the fixed frequency of 5kHz to see how g affects the filter gain at that frequency...

 

[gadagkar.rohit]

Hello RaulPinheiro,

Thanks for the reply.

Am I doing anything wrong here - b = [-0.2 0 0 0 1] and a= [1 0 0 0 -0.2]. or is my difference equation correct?

Thanks for you help

 

[RaulPinheiro]

y = g*y(n-N) - x + (1+g)*x(n-N);

y- g*y(n-N) = - x + (1+g)*x(n-N);

(1-z^-N)Y=(-1+(1+g)z^-N)X

H=Y/X=(-1+(1+g)z^-N) / (1-z^-N)

for N=5

b=[-1 0 0 0 0 (1+g)] (numerator)
a=[1 0 0 0 0 -1] (denominator)

note that for N=5, a and b are length 6

You must study some dsp in order to implement a filter.
Otherwise, u wont have a clue on what u're doing...

Raul

Hello RaulPinheiro,

Thanks for the reply.

Am I doing anything wrong here - b = [-0.2 0 0 0 1] and a= [1 0 0 0 -0.2]. or is my difference equation correct?

Thanks for you help

---------- Post added at 12:46 ---------- Previous post was at 12:44 ----------

CORRECTION

y = g*y(n-N) - x + (1+g)*x(n-N);

y- g*y(n-N) = - x + (1+g)*x(n-N);

(1-gz^-N)Y=(-1+(1+g)z^-N)X

H=Y/X=(-1+(1+g)z^-N) / (1-gz^-N)

for N=5

b=[-1 0 0 0 0 (1+g)] (numerator)
a=[1 0 0 0 0 -g] (denominator)

note that for N=5, a and b are length 6

You must study some dsp in order to implement a filter.
Otherwise, u wont have a clue on what u're doing...

Raul

 

[gadagkar.rohit]

Hi Raul,

Thanks for the reply. when i plotted the response of the filter that you gave. It looks like a multinotch filter.
I ve attached it. Please have a look.

 

[RaulPinheiro]

Hi Raul,

Thanks for the reply. when i plotted the response of the filter that you gave. It looks like a multinotch filter.
I ve attached it. Please have a look.

jdghjdjdjjtdujtuteutedyu