Lab Sept 27 review Fourier splits a signal

Lab Sept 27

review • Fourier splits a signal into components • Each component – Basis function – Coefficient • Basis function – sine wave at particular freq • Coefficient – amplitude and phase

review [ image taken from wikipedia ]

review [perfect sin waves at diff frequencies and amplitudes

review • Frequency domain graph

review • Frequency domain graph Number of cycles per area

review • Frequency domain graph 1 cycle. Height gives amplitude

review • Frequency domain graph 2 cycle. Height gives amplitude

review • Frequency domain graph 3 cycles. Height gives amplitude

review • Frequency domain graph 4 cycle. Height gives amplitude

review • Frequency domain graph

review spatial http: //local. wasp. uwa. edu. au/~pbourke/other/dft/ frequency

Spatial/frequency domain spatial http: //local. wasp. uwa. edu. au/~pbourke/other/dft/ frequency

More 2 D! • Spatial domain: – What we are used to

• Spatial domain More 2 D! y Pixel colour x

More 2 D! • Frequency domain v u Amplitude/phase

More 2 D! • Frequency domain v • u- freq in x direction • v- freq in y direction • amplitude is brightness u Amplitude/phase

2 d images. .

2 d images • Mixed components?

Handout quiz! • Groups! • Match each spatial graph to its frequency graph • What is the u, v value of each? Hint, only look at spatial graphs for this.

Pictures? • Frequency plot too complex to understand – But! We can see trends and particular properties

http: //www. cs. unm. edu/~brayer/vision/fourier. html

Edge effects • FFT is periodic – Assumes image repeats!

Edge effects • Why only in y direction? • Spike perpendicular to strong changes and features. http: //www. cs. unm. edu/~brayer/vision/fourier. html

Strong features http: //www. cs. unm. edu/~brayer/vision/fourier. html

Handout / quiz 2 • Match the image to the frequency graph