{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

eee508_Wavelets

# eee508_Wavelets - Wavelets a e ets Wavelets(signal...

This preview shows pages 1–3. Sign up to view the full content.

Wavelets Wavelets: (signal processing interpretation) ¾ A wavelet can be viewed as a bandpass filter with some upper and lower cutoff frequencies. ¾ ȥ ( t ) : “mother wavelet” or “a wavelet generating function” used to generate a set of bandpass filters that cover the frequency domain in which the signal of interest resides (signal processing interpretation). it i d t t t f b i t f i l it is used to generate a set of basis vectors for a signal expansion (mathematical interpretation). ± ² ± ² F T : < o m F.T. t \ EEE 508 1

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Wavelets ¾ Family of wavelets generated by shifting and scaling ȥ ( t ) 9 Scaling controls bandwidth and center frequency ± ² : < o m ¸ · ¨ § a a t F.T. 1 \ 9 Shifting allows us to view decomposition in terms of a convolution Basis consisting solely of scaled and shifted versions of a mother wavelet. ¹ © a a 9 Mother wavelet and generated wavelets in family are required to satisfy the “admissibility” condition: In frequency domain: ± ² : : < ³ f d 2 ± ² In time-domain: f ´ : f µ (bounded) Result: 0 0 < ³ f Note
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 9

eee508_Wavelets - Wavelets a e ets Wavelets(signal...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online