Physx32 t1_j5smg0x wrote on January 25, 2023 at 7:18 AM

Impulse function, δ(t) is defined as function whose value is infinite at t=0 and 0 elsewhere. So, Impulse function can be thought of as a signal which has a uniform amplitude of 1 throughout the frequency range. We give this signal as an input to the system (headphones) to find it's response for all the frequencies. The output given by the system is called the impulse response (the plot you posted). Now, if you compute the Fourier transform of the Impulse response, you'll get a complex function. The magnitude of this function is the frequency response of the system. Audiophiles are usually more interested in the frequency response than its time domain counterpart.

KuroFafnar t1_j5sp1me wrote on January 25, 2023 at 7:52 AM

Now explain like I’m five

audioen t1_j5sux24 wrote on January 25, 2023 at 9:12 AM

No ELI5 for this. Impulse response is the convolution that system applies to its input to produce its output. Convolution is a description of how prior data seen by the system alters the signal that is being produced right now. It is computed as integral of the input at past points multiplied with convolution function's value at corresponding time point. In sampled digital systems, both the impulse response and the signal are arrays of numbers, and you approximate the integral by placing the impulse response and input signal side by side, and you multiply input and impulse together at their corresponding positions, sum all the values together, and write the sum as the output sample. Then you move convolution function forwards along the input by one sample, and redo this massive calculation again to get the next output sample, and so on, and this is the convolution of the input with the impulse response.

As an example, guitarists may have amplifier cabinet simulators which are the sampled impulse responses of the speaker in the cabinet, which is usually open in the back, or possibly they have sampled room impulse responses and their effect processor actually convolves their playing with these impulses -- possibly multiple seconds long -- in real time to mimic the sound of these amplifiers and rooms. They actually perform the equivalent of the convolution computation in frequency domain because of the massive amount of multiplications that are needed for long impulses in time domain.

The ideal impulse response is infinitely narrow spike, because it means that the input at that one position is the only thing that affects the output and the convolution's output is thus the same as the input.

Physx32 t1_j5t2u64 wrote on January 25, 2023 at 11:02 AM

Impulse function is a signal that contains information for all frequencies from 0 to infinity. Since it contains this information, we give this as input to the headphone. The headphone then gives an output (which the OP posted). Now, we transform this output from time domain to frequency domain to see the frequency response of the headphone.