Question

In this assignment, you will simulate convolution by using Fourier Transform in Matlab. BACKGROUND: For continuous-time signals, the Continuous-Time Fourier Transform (CTFT) synthesis and analysis equations are given respectively as below. x(t) = \frac{1}{2\pi} \int_{-\infty}^{+\infty} X(j\omega)e^{jwt} d\omega X(j\omega) = \int_{-\infty}^{+\infty} x(t)e^{-jwt} dt CTFT describes aperiodic signals as a linear combination of complex exponentials occur at a continuum of frequencies, while CTFS can represent periodic signals as a weighted sum of complex exponentials occur at a discrete set of harmonically related frequencies \{k\omega_0\}. The response of an LTI system with impulse response h(t) to an input signal x(t) can be determined using Fourier transform as y(t) = \frac{1}{2\pi} \int_{-\infty}^{+\infty} X(j\omega)H(j\omega)e^{jwt} d\omega where H(j\omega) is the frequency response of the system and Y(j\omega) = X(j\omega)H(j\omega). Assignment: Given an LTI system with h(t) = e^{-at}u(t), a > 0, and the input x(t) = e^{-bt}u(t), b > 0, implement convolution by Fourier Transform using the symbolic toolbox. Hint: You may use fourier and ifourier functions in symbolic toolbox. Provide your Matlab code in your report and show the output signal y(t) using pretty.

          In this assignment, you will simulate convolution by using Fourier Transform in Matlab.
BACKGROUND: For continuous-time signals, the Continuous-Time Fourier Transform (CTFT)
synthesis and analysis equations are given respectively as below.
x(t) = \frac{1}{2\pi} \int_{-\infty}^{+\infty} X(j\omega)e^{jwt} d\omega
X(j\omega) = \int_{-\infty}^{+\infty} x(t)e^{-jwt} dt
CTFT describes aperiodic signals as a linear combination of complex exponentials occur at a
continuum of frequencies, while CTFS can represent periodic signals as a weighted sum of
complex exponentials occur at a discrete set of harmonically related frequencies \{k\omega_0\}.
The response of an LTI system with impulse response h(t) to an input signal x(t) can be
determined using Fourier transform as
y(t) = \frac{1}{2\pi} \int_{-\infty}^{+\infty} X(j\omega)H(j\omega)e^{jwt} d\omega
where H(j\omega) is the frequency response of the system and Y(j\omega) = X(j\omega)H(j\omega).
Assignment:
Given an LTI system with h(t) = e^{-at}u(t), a > 0, and the input x(t) = e^{-bt}u(t), b > 0,
implement convolution by Fourier Transform using the symbolic toolbox. Hint: You may use
fourier and ifourier functions in symbolic toolbox.
Provide your Matlab code in your report and show the output signal y(t) using pretty.

$In this assignment, you will simulate convolution by using Fourier Transform in Matlab. BACKGROUND: For continuous-time signals, the Continuous-Time Fourier Transform (CTFT) synthesis and analysis equations are given respectively as below. x(t) = (1)/(2π) ∫-∞^+∞ X(jω)e^jwt dωX(jω) = ∫-∞^+∞ x(t)e^-jwt dt CTFT describes aperiodic signals as a linear combination of complex exponentials occur at a continuum of frequencies, while CTFS can represent periodic signals as a weighted sum of complex exponentials occur at a discrete set of harmonically related frequencies {kω0}. The response of an LTI system with impulse response h(t) to an input signal x(t) can be determined using Fourier transform as y(t) = (1)/(2π) ∫-∞^+∞ X(jω)H(jω)e^jwt dωwhere H(jω) is the frequency response of the system and Y(jω) = X(jω)H(jω). Assignment: Given an LTI system with h(t) = e^-atu(t), a > 0, and the input x(t) = e^-btu(t), b > 0, implement convolution by Fourier Transform using the symbolic toolbox. Hint: You may use fourier and ifourier functions in symbolic toolbox. Provide your Matlab code in your report and show the output signal y(t) using pretty.$

Added by Gabriel W.

Question

Please give Ace some feedback