# What is Frequency response: Definition and 99 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. ### Engineering Frequency Response of High-Pass Filter at 1kHz

use a frequency range from 10 Hz to 10 kHz and show that the circuit operates as a high-pass filter with a ‘knee’ point at 1 kHz I have to be honest i an not 100% on what the question is asking me, should i be working out Frequency resonance first using all the information provided, then i need...
2. ### Engineering RLC circuit -- Phasor Transfer Function calculation

Good morning, I need some help solving those two question. I've attached my attempted solution below. Could i solve the transfer function any further? Thank you for your help
3. ### Automotive Amplitude based frequency response simulation in Abaqus

Hi, I have inputs like displacement of a driving mechanism and then the frequency of concern . Displacement: 0.2 mm Concerned Frequency: 100 Hz I would like to evaluate a part with the input displacement applied to a node and not as base excitation. It can be sweep over the frequency range...
4. ### Frequency Response Problem for given system

Hello, I am given an exercise in which I need to answer some questions, for this given system : y(n)=1/3[x(n)+x(n-1)] 1/ find the impulse response h(n), then H(n) 2/ calculate the magnitude ||H(n)|| and tell the nature of the filter 3/ calculate Fc which is cutoff frequency when Fe=8Khz , and...
5. ### Inverting op amp frequency response Bode plot help

Using analog discovery 2 kit and the bode plot produced by the network analyzer is off. The scope looks fine and everything is behaving how it should except for the bode plot. The magnitude of the bode plot will start at the correct dB then right before tapering off it shoots up a few dB and...
6. ### Engineering Frequency Response Between 100Hz and 100kHz

So am trying to find the Frequency response of a RC LPF between frequencies 100Hz-100kHz ,but i don't know what formula to use .
7. ### Engineering Magnitude versus Frequency Response Drawing from Pole-Zero Plot

Hi, EDIT: apologies for any ambiguity, but this is for DISCRETE systems, not analogue like the problem states. I was attempting a problem which is shown below . I am not really sure how to attempt this problem, but here is my attempt. Are there general methods for tackling these types of...
8. ### Frequency response - Hydraulic network

Hello everyone, i have a measured signal of a high pressure oscillation in a hydraulic network. Performing a FFT of said signal shows two dominant frequencies, a and b. After performing a linear analysis of the hydraulic network i found out that the network has two eigenvalues at those...
9. ### Frequency Response of a Damped Car-Suspension System

The quarter car system is represented by the above picture and I currently have all of the equations of motion and constants for each spring, mass, damper, distance, and moment of inertia. How can I find the frequency response with this information and knowing both tires hit a pothole of height...
10. ### Solving Differential Equation with Frequency Response

Homework Statement The AC response of an inductor can be modeled by the following differential equation: L \frac{di}{dt} + iR = V Find, using frequency response, the current of the system when the applied voltage V is: V = V_0 \sin(\omega t) Homework EquationsThe Attempt at a Solution In...
11. ### [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...
12. ### INA Frequency Response: Gain, Circuit & Open Loop Explained

1. QUESTION i'm dealing with a 3op instrumentation amplifier. say i have a circuit gain of 100 and i have an INA with a gain bandwidth product of 2MHz. the two buffer differential amplifiers are at 100k the open loop gain is then 2MHz/100k = 20 this frequency of 100k is going to effect the...
13. M

### Capacitors in Hybrid-pi Model and Frequency Response

This is what I have and I was wondering where C2 might go if I make apply the hybrid pi model on this circuit. I know that all the DC Voltages should be shorted if I were to make use of an equivalent circuit, so that in the hybrid pi model R1 should be in the input and R3 in the output. But what...
14. ### Question about an LTI System and its Frequency Response

Hello All, I am trying to learn about lti systems and what not for my research work but before I can apply my research I have to understand the fundamentals, which is what this question is kind of about! I want to find h(t), the impulse response of an LTI system where my input and output are...
15. ### 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...
16. ### 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...
17. ### A Obtaining Step Response for Linear Systems in Sinusoidal Frequency Domain

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.
18. ### Engineering Circuit analyse -- LR circuit frequency response

Homework Statement Find X [/B] Homework Equations V1(t)=8cos(12000t) V0(t)=Xcos(12000t+θ) The Attempt at a Solution [/B] I've tried quiet a lot actually, but all in vain. Seems like I am either misunderstanding something, or i am just too tired to think at the moment. Either way, I am...
19. ### Engineering How to Simplify a Frequency Response Circuit for Impedance Calculation?

Homework Statement Homework Equations V=IR H(w) = Y/F = Impedance of circuit The Attempt at a Solution I wanted to simplify this circuit before I find any impedance, but I am not sure if I did my source transformation correctly. Can i combine the f(t) current source with the 1ohm in...
20. ### How can I adjust the roll off of my preamp design for better frequency response?

Hello I am developing a low noise preamp and would like to change the roll off of my design to sharply decrease the gain for very low frequencies "1-5Hz". The results of my current design are as follows. I would need something that looked more like this.. I understand the simple equations...
21. ### 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...
22. ### How to graph the duffing frequency response

I`ve been able to use excel to plot the trajectory of a harmonically driven duffing oscillator for arbitrary parameters using Runge-Kutta method. I would like to do the same thing for the frequency response, but I simply can not figure out how. I am not very mathematically advanced so the first...
23. ### 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...
24. ### 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...
25. ### Find frequency response and circular frequency

Homework Statement We are given that system of 1st grade 1/2 * dy(t)/dt + y(t) = x(t) 1) We need to find frequency response { H(w) } 2) We need to find circular frequency -3dB 3) We need to find the absolute value of H(w) in dB for frequency f = 3/π Hz 2. Homework Equations (log is always...
26. ### Analytical Expressions for Frequency Response

Hi, I am struggling to understand the maths in the text shown below. (1) How does: r(t) = Acos(wt)+Bsin(wt) become; sqrt((A^2)+(B^2))cos(wt - arctan(B/A))? (2) He states that we can represent the input as a phasor and in one of three ways but doesn't say which one. (3) He then focus on the...
27. ### Frequency response of Torsional Vibration

Hello engineers! I have a project to measure/ obtain natural frequency of torsional vibration. Below is the detail: 1. Object measurement: Two rotor attached to one shaft and the shaft is supported by two bearing. The shaft is connected to a motor. I give the scheme below. 2. Equipment: two...
28. ### Frequency response of "purely ohmic" voltage divider?

I am trying to understand why/when a purely ohmic voltage divider (impedences Z1 and Z2 are both resistors) would have a delayed response for high-speed, transient changes in an input voltage? Whether the input is high-freq AC, or simply a square wave with a sharp rise or sharp drop, I've been...
29. ### Filter shape from poles and zeros

Hey guys, I am learning about the filter shapes deduced from the poles and zero plots, however a lot 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...
30. ### Transfer Function vs Frequency Response Function

Ive read other threads on here about this and am still slightly confused about it. I did a little experiment; and I am hoping someone can help shed some light on the results. The experiment: 1. Create a system: modeled after a simple spring-mass-damper with mass=1 damping zeta=.1, natural...
31. ### 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...
32. ### I have a question on the phase of a frequency response

Hello, I'm currently studying for an exam and came across a question I can't seem to figure out. How exactly do we go about calculating the phase of a frequency response. Here is the question, it for part A) iii. Here are the answers to the other parts and the sketch of the magnitude: I know...
33. ### Proving the Frequency Response of Notch Filter F(s)

Homework Statement Question is when F(s) = ## \frac {(s)^2+2*ζa*Wn*s+(Wn)^2)} {(s)^2+2*ζb*Wn*s+(Wn)^2)} \ ## prove that ## \ {|F(iw)|}^2 \ ## = 1 - ## \frac {4(ζb^2-ζa^2) \tilde w} {(1-\tilde w)^2+4ζb^2 \tilde w} \ ## when ## \tilde w \ ## = ## (\frac {w} {Wn} )^2 \ ## Homework Equations...
34. ### BJT Amp Frequency Response

I would like to know how to design an amplifier similar to the attached circuit with set -3db points, the lower on the order of 10Hz, and the higher on the order of 10kHz. I have designed amplifiers to work with a set gain, but have not dealt with frequency response before. I designed an amp...
35. ### Frequency response function of periodic-stiffness model of system

Hi, I'm analyzing a 3 dof undamped system with discrete springs and masses. Three of the springs have time-dependent stiffness, following periodic law (with period T), they are modulated at the same frequency but with a phase difference of 120 deg one from the other. So this is my system: (M *...
36. ### Why is my op-amp frequency response not ideal?

I am having a play about with the differential amplifier using a LM324 and have shorted both inputs and set them to 3V sine wave at 100Hz. i understand that in a ideal op-amp the output should be 0, how ever i am unsure of what is happening at the output... i increase the frequency every 1Khz...
37. ### Engineering Frequency response H(w) problem for rlc circuit

Homework Statement for the circuit below, compute frequency response H(w) using method of complex impedence. then if x(t) is input signal (we have equation but, say it is A*sin(wt), find y(t). Homework Equations transfer function H(w)=vout/vin The Attempt at a Solution R || L =...
38. ### Frequency Response: Understanding Signals & Systems

I'm doing my best to understand signals and systems. So I will give an example of what I'm talking about. you have a pressure transducer that has a 24vdc power supply and a voltage of 0-5vdc to measure the change in pressure, with the 0-5vdc connected to an analog to digital converter. With the...
39. ### Impulse response from frequency response

Homework Statement I am having some problems to derive Inverse Fourier transform of sinc function & exponential function. It's actually for getting the Impulse response from the given frequency response [which comprises of both sinc function & exponential function]. Also need to know the...
40. ### How to get (frequency response) from this [difference equation]?

Homework Statement Given this difference equation y(k) (of a bandpass FIR filter) ... y(k) = \frac{1}{K^2} \sum_{m = k-K+1}^k \; \sum_{n = m-K+1}^m x(n) - \frac{1}{L^2} \sum_{m = k-L+1}^k \; \sum_{n = m-L+1}^m x(n) ... how does one derive this frequency response H(f)? H(f) = \frac{1}{K^2}...
41. ### Engineering Need help finding frequency response of a circuit

I'm working on a problem which has two parts. 1. Find the frequency response function H(f) for a circuit. A hint given is to find H(s) first and then plug in s=j2\pi f to get H(f). 2. Find v_{out}(t), which is the response of the LTIC system to the periodic input signal v_{in}(t) =...
42. ### Finding Impulse Response of Frequency Response

Homework Statement Consider the frequency response H(e^jw) = e^j3w(5 + cos(w) + 2cos(w)). Find the impulse response h[n]. Homework Equations H(e^jw) = Ʃ(from k = 0 to M) bk * e^-jwk = Ʃ(from k = 0 to M) h[k] * e^-jwk The Attempt at a Solution So I'm not sure at all how to get...
43. ### Difficult Cascaded Op-amp frequency response problem

Homework Statement http://imgur.com/tJEPgbA http://imgur.com/tJEPgbA Homework Equations The Attempt at a Solution I started by focusing on the left Op-amp provided. My methodology to solve this question was essentially to assume a virtual short circuit so that the negative...
44. ### Frequency Response Homework: Impulse & Cosine Output

Homework Statement 3. (12 pts) Consider the causal FIR filter with {bk } = {1, 4, 5, 4, 1}. (a) What is the impulse response of this filter (in terms of delta functions)? (b) What is the frequency response of this filter? Simplify using Euler’s inverse formula. (c) What is the output y[n] of...

i would to know why whenever i increase my freq hertz, my gain db will decrease?
46. ### Engineering Frequency Response of Op amp Circuits

1. Homework Statement For this problem, the diagram of the circuit is attached. It was assigned to find the frequency response function of the circuit.2. Homework Equations E_o/E_i= -Zf/Zi3. The Attempt at a Solution I know for the top branch of the circuit, it has a negative feedback loop...
47. ### LTI systems- frequency response

I have attached an image of a ''brick-wall'' band pass filter. Can someone please help me find the expression of frequency response for it? Homework Statement Homework Equations The Attempt at a Solution
48. ### Obtaining Impulse Response & Frequency Response of LTI System

Homework Statement An LTI discrete-time system has frequency response given by (a) Use one of the above forms of the frequency response to obtain an equation for the impulse response h[n] of the system. (b) From the frequency response, determine the difference equation that is...
49. ### Signals: Fourier series and frequency response

Homework Statement A recursive DT system with input x[n] and output y[n] is given by y[n] = -0.25y[n-2] + x[n] a) Determine and plot the impulse response h[n] such that y[n] = x[n]*h[n] b) how would you classify the system and why? c) What modification, if any, should be made so...
50. ### External driving force on blackbox system: frequency response

External driving force on "blackbox" system: frequency response Easy question: I have a blackbox system (it's actually the Earth, but we can just treat it as a blackbox) driven externally by a periodic sinusoidal force (the Sun). If the driving force has a period of say 10 years, is there...