- 78 Views
- Uploaded on

Download Presentation
## PowerPoint Slideshow about ' Spectral Lines' - kay-jensen

**An Image/Link below is provided (as is) to download presentation**

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.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript

Spectral Lines

- Gives the frequency composition of the function
- Amplitude, phase of sinusoidal components

- Could provide information not found in time signal
- E.g. Pitch, noise components

- May help distinguish between signals
- E.g speech/speaker recognition

Spectral Lines Example

QUESTIONS --

DC Yes____ ao = ? No_____ ao = 0

Symmetry

Even____ an = ? bn = 0

Odd____ an = 0 bn = ?

Nether even nor odd ____ an = ? bn = ?

Halfwave symmetry

Yes_____ only odd harmonics

No______ all harmonics

Discontinuities

Yes_____ proportional to1/n

No______ proportional to1/n2

Note ? means find that variable.

Comment on the general form of the Fourier Series coefficients [an and/or bn.]

X

X

X

X

The Fourier Transform

- Applied to aperiodic signals
- Could be continuous or discrete
- Why Transform and not series?
- Do we want continuous or discrete?

The Fourier Transform

- Continuous Fourier Transform:

The Fourier Transform

- The Discrete Fourier Transform:

Fast Fourier Transform

- The Fast Fourier Transform (FFT) is a very efficient algorithm for performing a discrete Fourier transform
- FFT principle first used by Gauss in 18??
- FFT algorithm published by Cooley & Tukey in 1965
- In 1969, the 2048 point analysis of a seismic trace took 13 ½ hours. Using the FFT, the same task on the same machine took 2.4 seconds!

FFT in matlab

- Assign your time variables
- t = [0:255];

- Assign your function
- y = cos(2*pi*n/10);

- Choose the number of points for the FFT (preferably a power of two)
- N = 2048;

- Use the command ‘fft’ to compute the N-point FFT for your signal
- Yf = abs(fft(y,N));

- Use the ‘fftshift’ command to shift the zero-frequency component to center of spectrum for better visualization of your signals spectrum
- Yf= fftshift(Yf);

- Assign your frequency variable which is your x-axis for the spectrum
- f = [-N/2:N/2-1]/N; - this is the normalized frequency symmetrical about f0 and about the y-axis

- Plot the spectrum
- plot(f, Yf)

FFT in matlab

- Vary the fundamental frequency and see what happens

Download Presentation

Connecting to Server..