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How to get the impulse response from the frequency response?

Started by aliae ●December 2, 2014
Hi,

I have the frequency response near to the following form:

X(w) = 1/(1 + exp(wT1) + exp(wT2) + exp(T1+T2) )

where T1 and T2 are delays, to be prcise, T1= 1ms, T2 = 0.01 ms.

Now I want to find the time domain impulse response?, I know already it is
real squence.

I want to plot the frequency response using Matlab and then find the time
impulse response?

any suggestions or directions please?

	 

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Reply by aliae ●December 2, 20142014-12-02
>Hi,
>
>I have the frequency response near to the following form:
>
>X(w) = 1/(1 + exp(wT1) + exp(wT2) + exp(T1+T2) )
>
>where T1 and T2 are delays, to be prcise, T1= 1ms, T2 = 0.01 ms.
>
>Now I want to find the time domain impulse response?, I know already it

is

>real squence.
>
>I want to plot the frequency response using Matlab and then find the time
>impulse response?
>
>any suggestions or directions please?
>
>	 
>
>_____________________________		
>Posted through www.DSPRelated.com



I want to get the frequency response for the frequency range 0 Hz - 6000
Hz

	 

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Posted through www.DSPRelated.com
Reply by Tim Wescott ●December 2, 20142014-12-02
On Tue, 02 Dec 2014 14:15:46 -0600, aliae wrote:


> Hi,
> 
> I have the frequency response near to the following form:
> 
> X(w) = 1/(1 + exp(wT1) + exp(wT2) + exp(T1+T2) )
> 
> where T1 and T2 are delays, to be prcise, T1= 1ms, T2 = 0.01 ms.
> 
> Now I want to find the time domain impulse response?, I know already it
> is real squence.
> 
> I want to plot the frequency response using Matlab and then find the
> time impulse response?
> 
> any suggestions or directions please?


My first suggestion is that you double-check your frequency response 
equation.  If 'w' is the radian frequency, running from -infinity to 
infinity, then your frequency response is both very strange and goes to 
infinity as the frequency goes to infinity.

-- 

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com
Reply by Tim Wescott ●December 2, 20142014-12-02
On Tue, 02 Dec 2014 14:50:48 -0600, aliae wrote:


>>Hi,
>>
>>I have the frequency response near to the following form:
>>
>>X(w) = 1/(1 + exp(wT1) + exp(wT2) + exp(T1+T2) )
>>
>>where T1 and T2 are delays, to be prcise, T1= 1ms, T2 = 0.01 ms.
>>
>>Now I want to find the time domain impulse response?, I know already it
> is
>>real squence.
>>
>>I want to plot the frequency response using Matlab and then find the
>>time impulse response?
>>
>>any suggestions or directions please?
>>
>>
>>	 
>>_____________________________
>>Posted through www.DSPRelated.com
> 
> 
> I want to get the frequency response for the frequency range 0 Hz - 6000
> Hz


Hang on.  You say that you _have_ the frequency response, and you _want_ 
the impulse response.  Now you say that you _want_ the frequency response?

What do you have, and what do you want?

-- 

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com
Reply by aliae ●December 2, 20142014-12-02
>On Tue, 02 Dec 2014 14:50:48 -0600, aliae wrote:
>
>>>Hi,
>>>
>>>I have the frequency response near to the following form:
>>>
>>>X(w) = 1/(1 + exp(wT1) + exp(wT2) + exp(T1+T2) )
>>>
>>>where T1 and T2 are delays, to be prcise, T1= 1ms, T2 = 0.01 ms.
>>>
>>>Now I want to find the time domain impulse response?, I know already it
>> is
>>>real squence.
>>>
>>>I want to plot the frequency response using Matlab and then find the
>>>time impulse response?
>>>
>>>any suggestions or directions please?
>>>
>>>
>>>	 
>>>_____________________________




>>>Posted through www.DSPRelated.com
>> 
>> 
>> I want to get the frequency response for the frequency range 0 Hz -

6000

>> Hz
>
>Hang on.  You say that you _have_ the frequency response, and you _want_ 
>the impulse response.  Now you say that you _want_ the frequency

response?

>
>What do you have, and what do you want?
>
>-- 
>
>Tim Wescott
>Wescott Design Services
>http://www.wescottdesign.com
>


Yes, I have plot the frequency response of the above equation by sampling
the frequency variable ( w=2*pi*f), I just have plot it with frequency
variable f, is it correct to do so?,

 the second thing, I want to derive the impulse response of it, 	 

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Reply by robert bristow-johnson ●December 2, 20142014-12-02
On 12/2/14 4:11 PM, Tim Wescott wrote:

> On Tue, 02 Dec 2014 14:15:46 -0600, aliae wrote:
>
>> Hi,
>>
>> I have the frequency response near to the following form:
>>
>> X(w) = 1/(1 + exp(wT1) + exp(wT2) + exp(T1+T2) )
>>
>> where T1 and T2 are delays, to be prcise, T1= 1ms, T2 = 0.01 ms.
>>
>> Now I want to find the time domain impulse response?, I know already it
>> is real squence.
>>
>> I want to plot the frequency response using Matlab and then find the
>> time impulse response?
>>
>> any suggestions or directions please?
>
> My first suggestion is that you double-check your frequency response
> equation.  If 'w' is the radian frequency, running from -infinity to
> infinity, then your frequency response is both very strange and goes to
> infinity as the frequency goes to infinity.
>


i think he needs some j's in there, too.  and i'll bet it's gonna end up 
being some infinite echoey thing with T1, T2, and T1+T2 spacing of 
impulses in an sorta goofy "dirac comb".


-- 

r b-j                  rbj@audioimagination.com

"Imagination is more important than knowledge."
Reply by kaz ●December 2, 20142014-12-02
T1 = -10;
T2 = 10;
w = -.5:.01:.5;
X = 1./(1 + exp(w*T1) + exp(w*T2) + exp(T1+T2) );
plot(w,X);  %full Nyquist range

y = fftshift(ifft(X));
figure;
plot(real(y));

provided as is 
	 

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Reply by aliae ●December 2, 20142014-12-02
>
>T1 = -10;
>T2 = 10;
>w = -.5:.01:.5;
>X = 1./(1 + exp(w*T1) + exp(w*T2) + exp(T1+T2) );
>plot(w,X);  %full Nyquist range
>
>y = fftshift(ifft(X));
>figure;
>plot(real(y));
>
>provided as is 
>	 
>
>_____________________________		
>Posted through www.DSPRelated.com


I am sorry I have not explained the problem properly.

In fact I have modeled the wave propagation through different layers using
delays and reflection and transmission coefficients, and put them in matrix
form as follows
and then solving them to get the transmitted wave, since I have assumed
that my input is delta or one in frequency domain, the output will be the
frequency response. 
I have the matrix(2x2) that represent layer p:
TMp = 1/t* [ exp(-1i*w*T1)  r*exp(-1i*2*w*T1); r*exp(1i*w*T1) 
exp(1i*w*T1)];
 
and matrix(2x2) that represent layer j

TMj = 1/t* [ exp(-1i*w*T2) r*exp(-1i*w*T2); r*exp(1i*w*T2)  exp(1i*w*T2)];

t and r are scalar coefficients. Then I derive the transfer matrix multiple
p layers and multiple j layers


TM_DS = TMp*TMj*TMp*TMj*TMp*TMj*TMp*TMj*TMp*TMj*TMp*TMj*TMp;

Then my channel will be Ch = 1/TM_DS(1,1),

All the above are mathematics solution of the problem, but now in matlab I
would like to see the spectrum of the channel Ch, also evaluate the impulse
response(IR) of the Ch, where I have assume that the channel IR is real,

T1= 1 ms;
T2= 0.1 ms;

I have tried to do it but the spectrum it is not exactly what it should be,


	 

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Reply by ●December 3, 20142014-12-03
On Wednesday, December 3, 2014 9:15:50 AM UTC+13, aliae wrote:

> Hi,
> 
> I have the frequency response near to the following form:
> 
> X(w) = 1/(1 + exp(wT1) + exp(wT2) + exp(T1+T2) )
> 
> where T1 and T2 are delays, to be prcise, T1= 1ms, T2 = 0.01 ms.
> 
> Now I want to find the time domain impulse response?, I know already it is
> real squence.
> 
> I want to plot the frequency response using Matlab and then find the time
> impulse response?
> 
> any suggestions or directions please?
> 
> 	 
> 
> _____________________________		
> Posted through www.DSPRelated.com


No j terms?
Reply by Tim Wescott ●December 3, 20142014-12-03
On Tue, 02 Dec 2014 15:25:44 -0600, aliae wrote:


>>On Tue, 02 Dec 2014 14:50:48 -0600, aliae wrote:
>>
>>>>Hi,
>>>>
>>>>I have the frequency response near to the following form:
>>>>
>>>>X(w) = 1/(1 + exp(wT1) + exp(wT2) + exp(T1+T2) )
>>>>
>>>>where T1 and T2 are delays, to be prcise, T1= 1ms, T2 = 0.01 ms.
>>>>
>>>>Now I want to find the time domain impulse response?, I know already
>>>>it
>>> is
>>>>real squence.
>>>>
>>>>I want to plot the frequency response using Matlab and then find the
>>>>time impulse response?
>>>>
>>>>any suggestions or directions please?
>>>>
>>>>
>>>>
>>>>_____________________________
> 
> 
>>>>Posted through www.DSPRelated.com
>>> 
>>> 
>>> I want to get the frequency response for the frequency range 0 Hz -
> 6000
>>> Hz
>>
>>Hang on.  You say that you _have_ the frequency response, and you _want_
>>the impulse response.  Now you say that you _want_ the frequency
> response?
>>
>>What do you have, and what do you want?
>>
>>--
>>
>>Tim Wescott Wescott Design Services http://www.wescottdesign.com
>>
>>
> Yes, I have plot the frequency response of the above equation by
> sampling the frequency variable ( w=2*pi*f), I just have plot it with
> frequency variable f, is it correct to do so?,
> 
>  the second thing, I want to derive the impulse response of it,


X(w) does not look like a sane frequency response.

I suggest that you back off a bit, and tell us what you're actually 
working on (a siren, a dog door, an improved marital aid -- something like 
that).  Then maybe we can help you with the frequency response part, and 
we'll all go from there.

-- 

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com