Class Notes
(806,581)

Canada
(492,334)

McMaster University
(38,310)

Psychology
(4,968)

PSYCH 3A03
(56)

Paul Faure
(56)

Lecture

# Filters.docx

Unlock Document

McMaster University

Psychology

PSYCH 3A03

Paul Faure

Fall

Description

September 27 , 2013
Psych 3A03: Audition
Filters
Complex Sounds
- SO far we have been discussing sinusoidal motion and sine waves
- A sine wave is a very simple (homogenous) sound also known as a pure tone
signal
- Sine waves are the fundamental component of all other sound waves
- Most acoustic sounds, including animal vocalizations, are complex signals
- All complex sounds can be described as the sum of many simple sinusoidal
signals that differ in their amplitude, frequency, or phase
Jean Baptise Joseph Fourier
- The fourier series has since transcended its originally intended purpose,
spawning many new areas of study in mathematics and physics
Fourier Analysis
- When 2 or more sine waves are added together result is a complex wave
Discrete Fourier Analysis (Periodic Signals)
- All complex sounds can be described as the sum of many simple sinusoidal
signals that differ in their amplitude, phase and frequency
- If two signals are in phase and have the same frequency you end up with a
simple sound
- This is known as Fourier’s theorem
- ( ) ∑ ( ), where
n = integers from 1 to ∞ that represent the different numbers of
frequencies present in the complex signal
- Remember that ω = 20f (or ω = 20/T)
- By using known trigonometric identities the precious equation can be
rewritten as: ( ) ∑ ( ( ) ), for periodic signals
Time Domain Displays
- Spectra varies as function of the phase
- Looking at periodic vs. non periodic
Frequency Domain Displays
- Line or discrete spectrum
Why is this not continuous?
Fourier: the sum of sinusoids that describe a complex sound
Infinite signal which repeats; therefore, only the sum of the tree pure
tones present
- Continuous spectrum: pulse sound of discrete duration Peak in the magnitude is at 1000Hz which is the dominant frequency
Attenuates
Power as a function of frequencies
The phase spectrum all start at 0 for the frequency
1000Hz is the dominant frequency but we have to also explain the
occurrence of the pulse
To get the signal to be flat then pulsate at 1000Hz we need more
signals present at different relative amplitudes in order for them to
cancel and end up with a 20ms signal of 1000Hz
Square Wave
- Going to infinity in both directions
- Oscillates around 5
- Amplitudes are falling exponentially with increasing frequency
- Phase remains the same
- All of the integer multiples are present
The Making of a Square Wave
- Sine waves which are added to infinity
- Increasing frequencies and decreasing amplitudes
Square Wave
- 50% on 50% off: duty cycle
- Oscillation around 1; f 0 1
- f(target) = 1 + 2 + f3+ fn
Some Common Complex Waves
- Square wave
Fundamental a

More
Less
Related notes for PSYCH 3A03