# How to know the signal frequency from the digital filter output?

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#### feel_on_on

##### Full Member level 5
digital signal: 100,120.....input a FIR digital filter .....,output is 415,365,254...., i want to know what the output means?......digital filters filter some frequency....how i can know these frequency from the output digital:415,365,254....,

#### checkmate

Re: digital filter!

A digital filter is designed to filter the required frequencies. A digital filter is characterized by it's impulse response, it you input a unit impulse and record down its response. It may be finite or infinite. A finite response gives a FIR filter, while an infinite one will give an IIR filter.
The spectrum of the filter is derived by the fourier transform of the impulse response.

#### ali

##### Member level 2
digital filter!

You can approximate you filter Impulse responce by dividing H(jw) = output(jw)/input(jw) , but it may be not correct of all frequencies if you input does not contain some frequencies.

#### echo47

digital filter!

I think feel_on_on's question is more basic than that. He seems to be asking: what is a digitized signal?

Well, those data values are the signal's amplitude as each sample time. You need to know the sample rate to determine the sample times. Once you know the sample times, you can plot the data points on a time-line and see the signal's frequency.

Is that what you want to know?

#### feel_on_on

##### Full Member level 5
digital filter!

"the output digital:415,365,254 " means signal amplitude in some discrete time point? somes input:100,120 ,means input signal amplitude? really?...then..how to prove the filters correctly filter the frequency?

#### echo47

digital filter!

Welcome to the wild world of digital signal processing!

Let's say you are talking over a telephone that digitizes your voice at 8 thousand samples per second (8 ksps). If you whistle at 1 kHz, then the digitized signal may look like this. Notice how it repeats every eight samples, like points on a sinewave:
0, 141, 200, 141, 0, -141, -200, -141, 0, 141, 200, 141, 0, -141, -200, -141, ...

Now let's say you want to design a 1 kHz bandpass filter. Well, very basically, you write a program or design some digital hardware that passes signals that repeat every eight samples, and attenuates signals that repeat at some other rate. How to design such a thing? Well, grab yourself a book on digital signal processing and digital filter design!

How do you test such a filter? Well, there are all sorts of methods. One way, you can simply feed various frequency signals through it and observe what happens.

#### freeinthewind

digital filter!

I think it has 2 parts: the design of filter and the implementation of filter. the design of filter is easier.

#### swahlah

##### Full Member level 2
Re: digital filter!

Dear feel_on_on,
In order to know the filter is working correctly or not you should know the Impulse Response of the filter and then you can convolve the impulse response with the input signal to get the output signal in this way you can match the results. For this you need to run a test convolution function.
Now come on the second side when you know the input and output and you dont know the impulse resonse of the filter then it is an example of inverse problem. You should know how to solve inverse problem ... One simple technique that you can use is the deconvolution but it will not be the exact result and may be you can use some estimator......
I think simple deconvolution will help in your case if your filter is a linear one.

-Regards

#### checkmate

Re: digital filter!

I have already stated that the frequency response of the filter is the fourier transform of the impulse response.

#### swahlah

##### Full Member level 2
Re: digital filter!

Dear checkmate,
You are right that "frequency response of the filter is the fourier transform of the impulse response"
But it would be only possible when you have the filter in function.
But if we dont have the filter and only we have the input and output data then we can only find the filter function using inverse problem.

-Regards

#### checkmate

Re: digital filter!

swahlah said:
But if we dont have the filter and only we have the input and output data then we can only find the filter function using inverse problem.
Then just take the DFT of both output and input and divide them.

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