Can two different impulse responses give the same frequency response?

No. The impulse response and frequency response of an LTI system are related by the Fourier transform, which is one-to-one.

1. What is the relationship between impulse response and frequency response?
2. Can impulse response make the frequency response?
3. How do you find the frequency of an impulse response?
4. What is the frequency of an impulse signal?

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.

Can impulse response make the frequency response?

The impulse response is the response of a system to a single pulse of infinitely small duration and unit energy (a Dirac pulse). The frequency response shows how much each frequency is attenuated or amplified by the system. The frequency response of a system is the impulse response transformed to the frequency domain.

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).

What is the frequency of an impulse signal?

The true impulse has a much different magnitude spectrum. It is a constant value across all frequencies between 0 and f_s/2 Hz. Its phase spectrum is also a constant. As shown in one of the problems, the phase angle is 0.0 degree over the frequency range of 0 to f_s/2 Hz.