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I am preparing for my DSP exam and have this question about block diagram of DSP system: "Fsampling = 16 kHz, Delay = 4000 samples, Gain = 0.75. Provide impulse response of this system:" enter image description here

I assume that this is FIR filter, so impulse response would be finite. I tried drawing impulse response, how I assume it should look like for this system (sorry for my bad job, but I hope you could understand that). Is this correct? enter image description here

Also, if impulse has a 1 in 1000th sample, how would the output look? since there is no Gain on n (current) sample, impulse response would be 1 at 1000th sample ,then 0 and then 0.75 at 4000th sample?

Dominykas
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  • Well, the signals are discrete and you have drawn an impulse out that might come from an analog system. Can you simply focus on what is the formula for y[n] if you look at the diagram? How would a delay and sum be even able to produce your rounded waveform? – Justme Jan 07 '24 at 12:02
  • good point. I updated response for a digital system. I don't have any more data, but let's assume that x[n] = 0, if n = 1000, x[n] = 1. – Dominykas Jan 07 '24 at 12:09
  • Sorry I don't follow what you ask, and not the notation either. There is no output from sample 1000 in the system. Neither an input, unless you want to give it such an input for some reason. Which would just offset things by 1000 samples, but still. – Justme Jan 07 '24 at 12:12
  • Also you can't have an output pulse at sample 4000 if there was no pulse in to excite it. – Justme Jan 07 '24 at 12:18
  • I have to draw impulse response to this system. Input signal X[n] is not given, so I just assume that signal has impulse 1 at 1000 sample. I tried drawing quick impulse response and don't know if this is correct, because it looks like FIR filter block diagram, except it does not have gain block at the direct line. – Dominykas Jan 07 '24 at 12:20
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    x[n] can be anything, you are right. But why would you not test with an unit impulse, but with a weird signal with pulse delayed by 1000? Please, write down a formula for y[n] first, one path to x[n] at a time, to see it better. You only have one direct path and one delayed path with gain. And – Justme Jan 07 '24 at 12:28
  • formula for y[n] would be: Y[n] = X[n] + 0.75*X[n-4000]. But this doesn't really help, if we would analyze impulse signal when 1 is at x[0], Y[n] = 1, but then after 4000 samples Y[4000] would be 0.75 ? – Dominykas Jan 07 '24 at 12:37
  • I told it would help, you have it correct now. – Justme Jan 07 '24 at 12:42
  • huh, quite weird impulse response then. But yet again, this doesn't look like normal FIR filter so I guess it is possible. – Dominykas Jan 07 '24 at 12:54

1 Answers1

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You have it correct now.

It is a FIR system. It simply provides direct output, and attenuated output delayed by 4000.

Nobody claims it is a filter. For us humans, that would be maybe an echo effect for audio, because you hear a single delayed and attenuated echo after 250ms.

Justme
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