frequency response Definition and Topics - 9 Discussions

Frequency response is the quantitative measure of the output spectrum of a system or device in response to a stimulus, and is used to characterize the dynamics of the system. It is a measure of magnitude and phase of the output as a function of frequency, in comparison to the input. In simplest terms, if a sine wave is injected into a system at a given frequency, a linear system will respond at that same frequency with a certain magnitude and a certain phase angle relative to the input. Also for a linear system, doubling the amplitude of the input will double the amplitude of the output. In addition, if the system is time-invariant (so LTI), then the frequency response also will not vary with time. Thus for LTI systems, the frequency response can be seen as applying the system's transfer function to a purely imaginary number argument representing the frequency of the sinusoidal excitation.Two applications of frequency response analysis are related but have different objectives.
For an audio system, the objective may be to reproduce the input signal with no distortion. That would require a uniform (flat) magnitude of response up to the bandwidth limitation of the system, with the signal delayed by precisely the same amount of time at all frequencies. That amount of time could be seconds, or weeks or months in the case of recorded media.
In contrast, for a feedback apparatus used to control a dynamic system, the objective is to give the closed-loop system improved response as compared to the uncompensated system. The feedback generally needs to respond to system dynamics within a very small number of cycles of oscillation (usually less than one full cycle), and with a definite phase angle relative to the commanded control input. For feedback of sufficient amplification, getting the phase angle wrong can lead to instability for an open-loop stable system, or failure to stabilize a system that is open-loop unstable.
Digital filters may be used for both audio systems and feedback control systems, but since the objectives are different, generally the phase characteristics of the filters will be significantly different for the two applications.

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  1. B

    [Homework] Identify Filter type

    Homework Statement Identify the type of filter (kinds of frequencies the circuit filters out) analytically 2. The attempt at a solution I believe the top filter to be an inverting low-pass filter, which passes lower frequencies and blocks higher frequency signals. I also think that the...
  2. kostoglotov

    How transfer functions become Bode plots

    Homework Statement I have a question related to taking the logs of transfer functions, getting the individual Bode plots of each subsequent factor, and adding those plots graphically. I'm working from Fundamentals of Electric Circuits, 5th edt. Let me start with the following screen capture...
  3. G

    What is a problem of my graph?(frequency response)

    I have drawn a bode plot(freauency response), but it is not the same with one which is attatched in paper. Using this data, I have drawn the graph using matlab. I just put data into second order vibratoion system which is given in the paper(eq 18) Peak location of graph in paper is just in...
  4. Boudy

    A Linear Systems

    The transfer function of a linear system is known in the sinusoidal frequency domain. It is given in its final form as a complex function of the angular frequency ω (not jω ). How to obtain the step response? Thanks in advance.
  5. D

    Calculating the frequency response of filter with a matrix

    Homework Statement This is actually part 3 of the question. Part one was to form 7 equations to form a 7x7 matrix, part 2 was to solve it, which I've done. This question is to be done with Matlab, by the way. Part 3: Homework Equations Frequency response = Vout / Vin. The Attempt at a...
  6. Captain1024

    Finding Impulse And Frequency Responses

    Homework Statement Consider a LTI system defined by the following difference equation: ##\mathrm{y}[n]=-2x[n]+4x[n-1]-2x[n-2]## a) Determine the impulse response of the system b) Determine the frequency response of the system Homework Equations DTFT...
  7. Captain1024

    Find the Output of an LTI System Given Input and Impulse Response

    Homework Statement Consider a LTI system for which the filter coefficients are ##{\mathrm{h}_k}=\{1,2,1\}##. Find the output when the input is ##\mathrm{x}[n]=3\mathrm{cos}(\frac{\pi}{3}n-\frac{\pi}{2})-3\mathrm{cos}(\frac{7\pi}{8}n)##. Identify two frequencies in this composite signal. Show...
  8. C

    Filter shape from poles and zeros

    Hey guys, I am learning about the filter shapes deduced from the poles and zero plots, however alot of sources are describing it differently with no logical explanation. I want to know what exactly the poles and zeros do between the range Ω = 0 and Ω = π. One source i read explains if the pole...
  9. V

    Calculating half power frequency/cutoff frequency

    Homework Statement *(Problems attached as images)* For first problem: ##\cfrac{|V_2|}{|V_1|} = \cfrac{1}{\sqrt{4+(\omega RC)^2}}## For second problem: ##\cfrac{|V_2|}{|V_1|} = \cfrac{\sqrt{1+(\omega RC)^2}}{\sqrt{4 + (\omega RC)^2}}## I have to calculate half power frequency for both...