Mathematics Homework Solutions

Inverse Fourier transform

Find the inverse Fourier transform of each of the following Fourier transforms: X(w) = cos(2w) X(x) = jw

Inverse transform

Find the inverse Fourier transform of each of the following Fourier transforms: X(x) = jw The answer I have is x[n] = (-1)^n / n (for n not equal to zero) 0 (for n = 0) I don't know how to get there.

Fourier Transforms

Using Fourier transforms where possible, derive the Fourier transforms of the following functions using the relationship: F(fx) = ∫ f(x)*exp[-i2πfxx]dx a.) f(x) = δ(x-a) b.) f(x) = cos(x-ø) c.) f(x) = αsin(ax) keywords: integration, integrates, integrals, integrating, double, triple, multiple

Fourier transform

Using Fourier transforms where possible, derive the Fourier transforms of the following functions using the relationship: a.) f(x) = exp[i2po(x/lamda)sin(theta)] b.) f(x) = exp(- /ax/ ) See the attached file for full description.

Discrete Time Fourier Transform with Matlab

Please see the attached file for full description. Calculate by hand the X(omega), DTFT of the sequence x[n]=[1 1 1 1 0 0 0 0] for n=0:7, zero else. Using Matlab, plot the real and imaginary components of your result for X(omega) for omega=0:0.01:2*pi, one plot for the real, one part for the imaginary. On the same plot ...continues

matlab plot

(See attached file for full problem description) For sequence x[n]=[1 1 1 1 0 0 0 0] for n=0:7, so N=8 Using above x[n]: a) stem(x); b) Use the shift theorm to plot x delayed by 1, 4, 5, 6, and 8 samples, and plot the result for each. Remember the shift theorem says a delay by t0 seconds is equal to multiplying the spe ...continues

Fourier coefficients

Fourier coefficients / b1, b2, b3, b4, b5... b11. -------------------------------------------------------------------------------- I have an output of an electronic device (full wave rectifier) that gives a sine wave with the negative part transposed symmetric to xx so that the function is always positive. I have to find the f ...continues

Finding Trigonometric Fourier Series without doing any integration

Find the trigonometric Fourier series of the signals without doing any integration. See the attached file for full description.

Inverse Fourier Transform

See attached file for full problem description. X(f) = 10 [sinc2f/(3 + j2*pi*f)]

Fourier Transform Integrals

Using the Fourier transform integral, find Fourier transforms of the following signals. xa(t) = t *exp(-αt) * u(t), α > 0; xb(t) = t2 * u(t) * u(1 – t) xc(t) = exp(-αt) * u(t) * u(1 – t), α > 0;

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