ECET345 Week 7 Homework Assignment
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Buy here: http://student.land/products.php?product=ECET345-We ek-7-Homework-Assignment A sine wave of 60 Hz, amplitude of 117 V, and initial phase of zero (or 117 sin(2π*60t) is full wave rectified and sampled at 2,048 samples per second after full wave rectification. Research the Fourier series for a full wave rectified sine wave (on the Internet or in circuit theory books, such as Linear Circuits by Ronald E. Scott) and write it below. Then write a MATLAB program that samples and stores 4,096 points of full wave rectified sine wave and performs Fourier analysis (FFT) of the full wave rectified sine wave on the stored points. Plot the results in both linear and log scale (in two separate figures) and extract the amplitude of the DC component and the first four harmonics (first , second, third, and fourth multiple of the fundamental frequency) of the Fourier analysis, then enter them in the table given below. The DC component is given by the first number in the Fourier analysis. Hint: Full wave rectification can be achieved in MATLAB simply by taking the absolute value (abs command) of the sine wave. Given a cosine wave of frequency (1/π) Hz and amplitude of 10, sampled at 10 samples/second, express it in a complex exponential form. Using Euler’s formula, , A periodic sequence (i.e., a sequence continuing forever) is given by f(nT) = [ 0011 0000 1100 0011 0000 1100 …….]. A signal is sampled at 1,024 samples/second and you have collected and stored 32,768 samples after sampling. You apply the FFT algorithm to it, using all of the stored data. What will be the
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Transcript of ECET345 Week 7 Homework Assignment
Buy here: http://student.land/products.php?product=ECET345-Week-7-Homework-Assignment
A sine wave of 60 Hz, amplitude of 117 V, and initial phase of zero (or 117 sin(2π*60t) is full
wave rectified and sampled at 2,048 samples per second after full wave rectification. Research
the Fourier series for a full wave rectified sine wave (on the Internet or in circuit theory books,
such as Linear Circuits by Ronald E. Scott) and write it below.
Then write a MATLAB program that samples and stores 4,096 points of full wave rectified sine
wave and performs Fourier analysis (FFT) of the full wave rectified sine wave on the stored
points.
Plot the results in both linear and log scale (in two separate figures) and extract the
amplitude of the DC component and the first four harmonics (first , second, third, and fourth
multiple of the fundamental frequency) of the Fourier analysis, then enter them in the table given
below. The DC component is given by the first number in the Fourier analysis. Hint: Full wave
rectification can be achieved in MATLAB simply by taking the absolute value (abs
command) of the sine wave.
Given a cosine wave of frequency (1/π) Hz and amplitude of 10, sampled at 10 samples/second,
express it in a complex exponential form.
Using Euler’s formula, ,
A periodic sequence (i.e., a sequence continuing forever) is given by
f(nT) = [ 0011 0000 1100 0011 0000 1100 …….].
A signal is sampled at 1,024 samples/second and you have collected and stored 32,768 samples
after sampling. You apply the FFT algorithm to it, using all of the stored data. What will be the
frequency resolution of the FFT in hertz? Hint: See the Week 7 Lecture for the definition of
resolution of FFT.
You are required to sample a signal consisting of a mixture of 10, 10.25, and 12 Hz sinusoids
that you want to be able to resolve in your Fourier (spectrum) analysis. Your data acquisition
hardware can store up to 32,768 samples. Assuming that you store all 32,768 samples, what is
the range of sampling frequencies such that you neither violate the Nyquist theorem nor go
above the needed resolution?
