Relationship between Frequency response, magnitude spectrum and gain

1. Is gain the same as magnitude?
2. What is the magnitude of frequency response?
3. How do you find the magnitude of a frequency response?
4. What is frequency response formula?

Is gain the same as magnitude?

It is defined as the magnitude (gain), and phase differences between the input and the output sinusoids. To plot the frequency response, a vector of frequencies is created first (varying between zero or "DC" and infinity), and compute the value of the transfer function at those frequencies.

What is the magnitude of frequency response?

The frequency response is characterized by the magnitude, typically in decibels (dB) or as a generic amplitude of the dependent variable, and the phase, in radians or degrees, measured against frequency, in radian/s, Hertz (Hz) or as a fraction of the sampling frequency.

How do you find the magnitude of a frequency response?

First we substitute s = jω into H(s) to obtain an expression of the frequency response. Note that the numerator and the denomator are both complex. To obtain the amplitude response, we take the absolute value of H(jω). To do this, we evaluate the magnitude of the numerator and the denominator separately.

What is frequency response formula?

This can be solved for the frequency response, H(ω) = e ^jωn (b₁ + b₂ e ^-jω + b₃ e ^-2jω)/ e ^jωn (a₁ + a₂ e ^-jω + a₃ e ^-2jω). This form of the frequency response can be generalized to LTI difference equations with an arbitrary number of terms.