How to compute the impulse response from incomplete frequency response data?

1. What is the relationship between impulse response and frequency response?
2. How do you calculate impulse response from output?
3. How do you find the frequency of an impulse response?
4. How do you calculate impulse response in DSP?

What is the relationship between impulse response and frequency response?

The relationship between the impulse response and the frequency response is one of the foundations of signal processing: A system's frequency response is the Fourier Transform of its impulse response.

How do you calculate impulse response from output?

Given the system equation, you can find the impulse response just by feeding x[n] = δ[n] into the system. If the system is linear and time-invariant (terms we'll define later), then you can use the impulse response to find the output for any input, using a method called convolution that we'll learn in two weeks.

How do you find the frequency of an impulse response?

The frequency response of the system (also called the transfer function of the system) is given by the Fourier transform of the impulse response, so H(ω) = F h(t). Thus the impulse response can be found by taking the inverse Fourier transform of the impulse response: h(t) = F−1 H(ω).

How do you calculate impulse response in DSP?

If we set x[n] = δ[n], then the output y[n] will be the response of the system to an impulse, or simply, the "Impulse Response".