Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

According to Fourier%u2019s Theorem, any periodic signal can be constructed from

ID: 3345143 • Letter: A

Question


According to Fourier%u2019s Theorem, any periodic signal can be constructed from a sum of sine and cosine functions. For example, a triangle wave can be constructed from the following Fourier series:



Construct a 4-term (that is, n=1,3,5,7) pseudo-analog approximation of a triangle wave with a fundamental frequency of 100 Hz. Make the triangle wave 30 ms long. (The pseudo-analog signal should be constructed with a sampling frequency of 100000 Hz.) What is the Nyquist rate for this signal?


I need to know what s(t) is equal to when n = 1,3,5,7

Explanation / Answer

Sorry, the 10 ms triangular wave is (extending 5 ms both sides of t =0 and no dc): x(t) = (t + 0.0025)/0.005 for (-0.005 0.005) { x(t). sin (n * 2*pi*100*t) dt } Difficult (for me) to proceed further ... Also, I am not able to fully see your question (there is something missing below): According to Fourier%u2019s Theorem, any periodic signal can be constructed from a sum of sine and cosine functions. For example, a triangle wave can be constructed from the following Fourier series: Construct a 4-term (that is, n=1,3,5,7) pseudo-analog approximation of a triangle wave with a fundamental frequency of 100 Hz. Make the triangle wave 30 ms long. (The pseudo-analog signal should be constructed with a sampling frequency of 100000 Hz.) What is the Nyquist rate for this signal?