Richard M. Stern demo January 12, 2009

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Presentation transcript:

SIGNAL PROCESSING: SOME APPLICATIONS IN SPEECH, MUSIC, and IMAGE PROCESSING Richard M. Stern 18-396 demo January 12, 2009 Department of Electrical and Computer Engineering and School of Computer Science Carnegie Mellon University Pittsburgh, Pennsylvania 15213

What is signal processing? Oppenheim and Schafer’s definition (1999): [The discipline that is concerned with] the representation, transformation, and manipulation of signals and the information they contain

Why perform signal processing? To understand the content of signals To represent signals in a form that is more insightful to us To transform signals into a form that is more useful to us

Representation of speech in time domain

Representation of speech in frequency domain

Signal representation: turning sine waves into square waves

Signal processing in human speech production: the source-filter model of speech A useful model for representing the generation of speech sounds: Amplitude Pitch Pulse train source Noise source Vocal tract model p[n]

Speech coding: separating the vocal tract excitation and and filter Original speech: Speech with 75-Hz excitation: Speech with 150 Hz excitation: Speech with noise excitation:

Representation and filtering of speech sounds

Linear filtering the waveform x[n] y[n] Filter 1: y[n] = 3.6y[n–1]+5.0y[n–2]–3.2y[n–3]+.82y[n–4] +.013x[n]–.032x[n–1]+.044x[n–2]–.033x[n–3]+.013x[n–4] Filter 2: y[n] = 2.7y[n–1]–3.3y[n–2]+2.0y[n–3–.57y[n–4] +.35x[n]–1.3x[n–1]+2.0x[n–2]–1.3x[n–3]+.35x[n–4]

Filter 1 in the time domain

Output of Filter 1 in the frequency domain Original: Lowpass:

Filter 2 in the time domain

Output of Filter 2 in the frequency domain Original: Highpass:

What happens when we filter images?

Lowpass filtering with a Gaussian kernel ….

Not enough blur??

We can also highpass filter ….

… and threshold to detect the image edges