Impulse Response PDF Synthesis of a square-wave:

Fourier Series

2.3 Approximating with Fourier Sine Series. A MATLAB code is used to plot the square wave function along with the Fourier sine series in order to compare the.

EE 321 Example of Truncated Fourier Series Fall 2012 The Matlab

Example of Truncated Fourier Series. Fall 2012. The Matlab code below computes and plots a truncated Fourier series for a square wave defined over one period

Fast Fourier Transform and MATLAB Implementation

Example 4: Square Wave. 0.5. 1. Square Wave Signal. Fs = 150; % Sampling frequency t = 0:1/Fs:1; % Time vector of 1 second f = 5; % Create a sine wave of f Hz.

Constructing Waveforms from Fourier Series using MATLAB

for the sawtooth waveform shown below

PRELAB

MATLAB of the. Fourier series representation of the square wave from Question 2. For the five plots truncate the series so that it only contains the first q ...

Computing Fourier Series and Power Spectrum with MATLAB

coefficients except for a0 will be zero providing another simple check. Let's try computing a Fourier series for a square wave signal that is on for half the.

Fourier Series Square Wave Example

Fourier Series Square Wave Example. The Fourier series of a square wave with period 1 is f(t)=1+. 4 π с. ∑ n=1 n odd sin(πnt) n. In what follows we plot.

Fourier Series MATLAB GUI Documentation

Frequency content of square wave sample signal and its approximation. You can clearly see that the user-defined signal's frequency spectrum consists of five

Lecture 4&5 MATLAB applications In Signal Processing

Fourier Series. • Example 1: • Using Fourier series expansion a square wave with a period of 2 ms

Title of Document (Times New Roman 16 pt

This model is controlled by the Fourier Series MATLAB GUI. The Go back to the Fourier Series GUI and insert these values; the result resembles a square wave.

Fourier Series

A MATLAB code is used to plot the square wave function along with the Fourier sine series in order to compare the accuracy and error between the approximation

PRELAB

Derive the Fourier series representation for the square wave shown in Figure The following MATLAB script plots the first q = 50 terms of Fourier series.

Fast Fourier Transform and MATLAB Implementation

In the fields of communications signal processing

Constructing Waveforms from Fourier Series using MATLAB

Find the Fourier series expression for the sawtooth waveform shown below

Lecture 4&5 MATLAB applications In Signal Processing

Using Fourier series expansion a square wave with a period of 2 ms

Computing Fourier Series and Power Spectrum with MATLAB

you how you can easily perform this analysis using MATLAB. Let's try computing a Fourier series for a square wave signal that is on for half the.

ECEN 314: Matlab Project 1 Fourier Series Synthesizer

8/04/2013 2.1 A Signal Generator Based on CT Fourier Series ... Let ak be the Fourier series coefficients of a periodic square wave with T = 1 defined ...

EE 321 Example of Truncated Fourier Series Fall 2012 The Matlab

The Matlab code below computes and plots a truncated Fourier series for a square wave defined over one period of T seconds as.

Impulse Response

Synthesis of a square-wave: Run MATLAB demo on MATLAB/ Graphics/ generating square wave from sine waves. 34. Calculate the Continuous-Time Fourier Series

Indian Institute of Information Technology Allahabad Department of

Objective – Write MATLAB code to study sine cosine Fourier series rep- resentation of a square wave with fundamental period 2 and unity amplitude.

EE 470 - BIOMEDICAL SIGNALS AND SYSTEMS

Active Learning Exercises - Part 2

29. For the system whose block diagram presentation given please determine:

- The differential equation - The characteristic polynomial - Eigenvalues and eigenfuctions - The transfer function - The impulse response - Stability of the system - Steady-state output for x(t)=u(t) - Steady-state output for x(t)=cos(20t) - Step response

30. Plot the impulse and step responses of the system in question-29 using

- functions you determined above - step and impulse functions of the MATLAB

31. A linear time-invariant system is required to realize the impulse response

shown in the figure. a) Design the system in block diagram, differential equation and transfer function form b) Determine the system parameters from the figure c) Modify the system so that its step response reaches its steady-state value in the shortest time d) Draw the step responses for the unmodified and modified system together 2 2.5

1.5 x(t) y(t)

00.050.10.15 0.250.30.350.4

-60 -40 -20 0 20 40
60
80

100Impulse Response

Time (sec)

Amplitude

Figure for question 31

2 showing carefully all critical amplitude and time values for the plots

32. The antibiotic ampicillin (600 mg) needs to be added intravenously repeatedly

in order to treat a certain infection, the drug is ineffective if it drops below a bloodstream concentration of 0.0001 mg/ml and has some toxic side effects if its concentration exceeds 0.055 mg/ml. You have been asked to determine what happens to the concentration of the drug in the body as a function of time and to determine the best time interval between injections. The drug is expensive. You are given the following information: - The body's fluid volume is 12 liters, - A certain fraction is eliminated from the body by the kidneys, - A certain fraction is eliminated from the body by metabolism, - 4 hours after initial injection, the concentration of ampicillin in the blood is 0.0005 mg/ml, - 4 hours after the initial injection, the concentration of ampicillin in the urine is 0.002 mg/ml.

Based on the information given:

a) Develop a model to solve the above problem. You may develop a MATLAB script or an EXCEL spreadsheet to execute the model, graphing the drug concentration as a function of time, b) What are the fractions of antibiotic removed by the kidneys and by metabolism? c) What is the time interval that you would recommend? d) What are the upper and lower bounds to your answer? e) Which parameters affected your model the most?

33. Synthesis of a square-wave: Run MATLAB demo on MATLAB/ Graphics/

generating square wave from sine waves.

34. Calculate the Continuous-Time Fourier Series for

- x(t) = 2 + 2cos(0t) + 2sin(0t) with 0= 2 - x(t) = cos(2t)sin(3t) and graph its amplitude and phase spectra - Download and run FS_ALE_28_03_2005.m

35. Obtain the complex (exponential) Fourier series representation of the

following functions and draw their line spectra - A square wave (FS_square_wave.m) - A rectangular wave (FS_rectangular_wave.m) - A triangular wave (FS_triangular_wave.m)

36. CTFS of an impulse train and a rectangular pulse sequence using properties of

F series. Determine CTFS expansion of following functions: - an impulse train n nTttx 01 )( (q1_FS_dirac.m) - a shifted impulse train n nTTttx 00 2 4)( (q2_FS_dirac.m) nn nTTtnTTttx 00 00 3 44)(
(q3_FS_dirac.m) dxtx t 34
(q4_FS_dirac.m)

37. For the RC low-pass filter shown determine:

- The impulse response V 0 V i R C 3 - The transfer function - The frequency response function

38. For the RLC type band-pass filter shown

- Obtain and draw the impulse response - Determine the frequency response function

39. Fourier transform of x(t) = (t+1) - (t-1)

is a) 2jsin() b) 1 c) 0 d) 2cos() e) None of the above, they are ....

40. If ][)(kXtx

FS then Y[k] for y(t)=x(t-2)+x(t+2) is The Fourier transform of signal shown is a) )2sin(][ F kX b) )2cos(][2kkXkj F c) )2cos(][2 F kkX d) F kj ekX 2 ][2 e) None of the above, it is ...

41. The Fourier series coefficient X[3] for x(t) = 2 + cos(2t) + 3sin(5t) is

a) 0 b) 0.5 c) 1.5j d) 2 e) None of the above, it is ...

42. Assume that the signal in question 3 is a voltage applied to 1- resistor. The

total signal power is a) 6 Wquotesdbs_dbs4.pdfusesText_8

[PDF] Impulse Response Synthesis of a square-wave: