# Week 3 Part 1

## 37 terms

### Fourier Transform

1. when we use techniques that Fourier developed
2. creates a spectrum from a time domain waveform (such as a microphone signal) that shows what the individual components are
3. a way to go from one view of a signal to another view- from Time domain to Frequency domain

### Time Domain Data

-waveform that you see when you have a microphone recording on a screen in front of you
-Y axis: amplitude
-X axis: time

### What happens if you subject the time domain waveform to the Fourier Transform?

you end up with a Frequency Domain Display that shows a spectrum which represents a slice in time, or a snapshot in time
-Y axis: amplitude
-X axis: frequency

### Time Domain Data characteristics

- a waveform represents sound directly
- air pressure changes over time

### How do we get a Frequency Domain display?

take the Time Domain waveform and do a Fourier Transform to give us a spectrum display

### Frequency Domain display

-spectrum has split individual sounds out of the combined total
-Y axis: amplitude
-X axis: frequency

### What is the great benefit to the Frequency Domain display?

shows us what individual components of one sound are, as well as the relative proportions of each

### Frequency Domain Data

a line spectrum shows the frequency components of a periodic sound

### Harmonic Series

exact multiples of the fundamental frequency, with no energy between the individual harmonic components

### Describe the sound source that comes out of the larynx.

-a fundamental, then harmonics that are exact multiples of that fundamental
-although the human voice is imperfect, so there will be some noise mixed in there too
-upper harmonics get weaker as the frequency gets higher

### Is the human voice periodic?

Yes, nearly periodic

### What happens to the upper harmonics as they go up in frequency?

they get progressively weaker

### Characteristics of Periodic Signal Spectrum

-frequency domain description of the signal
-has harmonics that are multiples of the Fundamental
-has nothing between the lines
-lines represent the harmonic frequencies

### Time vs. Frequency Display

displays both time domain and frequency displays on the same screen
-top of the screen: time domain
-bottom of screen: spectrum
X axis: frequency
Y axis: amplitude

### What do the peaks of the spectrum of the time vs. frequency display represent?

individual harmonic components of the signal

### What changes do you see on the spectrum of the time vs. frequency display when you make your voice softer or louder?

changes in relative strength of the harmonics

### What changes do you see on the spectrum of the time vs. frequency display when you raise and lower your pitch?

you'll see the harmonics spreading apart from one another or coming back together as the pitch comes back down again

### What does a spectral display represent?

represents the frequency components that are present in a sound

### How do complex periodic signals look in a spectral display?

they have multiple lines

### What would noise look like in a spectral display?

it would have all frequencies present with various different phase relationships to each other with approx equal amplitude

### sine wave

single line on a spectrum

multiple lines

-all frequencies
-equal amplitude
-random phase

### Spectral envelope

encloses an area that would have been completely filled in by vertical lines representing individual sine waves
-shows us the relative strength of the different frequency components in noise

### Is the voice source truly periodic?

-nearly periodic
-there is some spread around the base of the peaks which represents the imperfections or noise that is present in every human voice

### Harmonics to Noise Ratio

ratio of the height of harmonic components to the level of noise between them

### Fast Fourier Transform

-shows us the range of harmonics present in each sound
-peak for each of those harmonics

### What is FFT useful for?

-displaying features of the sound source
-not so much about the vocal tract filter

### Linear Predictive Coding

-shows a spectral envelope, but not individual harmonics
-no details of the sound source (sound could be phonated or whispered), but revealing of what the vocal tract filter is doing
-shows what vocal tract is doing- what its resonance frequencies are relative to one another

### LPC

Linear Predictive Coding

### FFT

Fast Fourier Transform

### How does a FFT spectrum look?

has individual peaks that are harmonic components- spaced equally because they are multiples of the fundamental

### How does a LPC spectrum look?

don't see individual harmonics, but do see peaks which are formants

### Spectrum

-shows the ingredients of a sound at a single point in time
-because it's not a Time Display, it can't show the progression of that signal over time

### Spectrogram

-can show individual slices that are arranged side by side over time
-lines up a series of successive spectral slices next to one another which will show how the frequency components of a sound changed over time

### Why is a spectrogram sometimes called a 3D spectrogram?

it can display 3 different parameters at a time

### What parameters does a spectrogram display?

-X axis: time
-Y axis: frequency
-whether the line is lighter or darker represents the intensity of the signal (darker= stronger intensity)