Chapter 7 - DSP Based Testing. Outline. Trigonometric Fourier Series (FS) Discrete-Time Fourier Series (DTFS) Relationship to FS Working directly with samples Complex form Discrete Fourier Transform (DFT) Fast Fourier Transform (FFT) Applications Equivalence of Time and Frequency Domains
Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
3 fFourier Analysis Of Periodic SignalsTrigonometric Form
Split into 2 parts:
To simplify further, use
Replace infinite summations with single parameter:
Used for spectral plot purposes
FS = 100 kHz
The samples of a periodic signal can be described in matrix form as:
From which the spectral coefficients are found from:
Conversely, given the spectral coefficients, the original samples can be determined through an inverse operation given by
This inverse operation can be computed using an inverse FFT.
Fourier Transform Samples (N=8):
Complex Form for DTFS
Trigonometric Form for DTFS
Add NZ zeros