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Linear Systems.docx

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McMaster University
Paul Faure

October 1 , 2013 Psych 3A03: Audition Linear Systems Amplitude Modulated (AM) Stimulus - Amplitude modulation can also occur by modulating the amplitude of a single sine wave - Let A vary sinusoidally as a function of time: A(t)=[1+msin(2πF t)] m - D(t) = A[1+msin(2πF t)]min(2πF t) c Frequency Modulated (FM) Stimulus - Spectrogram: shows the spectrum (frequency) and timing information - Amplitude can be shown by the thickness of the line Spectrogram: Combined Information - Amplitude information is colour coated on a frequency vs. time graph Noise - Common stimulus used in research - Used as a masking signal or to control background noise or making sure that we are not providing any amplitude - Mean energy is centered on 0 but there are large deviations Noise, Amplitude and Bandwidth - Amplitude: Instantaneous amplitude signal is random within specified frequency band - Spectral bandwidth  Narrowband noise (NBN): relative signal bandwidth is small  Wideband noise (WBN): relative signal bandwidth is large Amplitude Modulated Noise - Less than random fluctuations - Shaping the noise with different frequency envelope - Gausian noise can also be amplitude modulated - Rectification: all amplitudes as positive by taking the square Measuring Noise Amplitude - Total power:  Amplitude of all sinusoidal components in noise signal  BW – signal bandwidth  I = signal intensity (not in dB)  TP = BW x I - Spectrum Level (N ) 0  Average noise intensity in a band of noise 1Hz wide  N 0 spectrum level of signal  Average power/ Hertz  N = TP/BW 0 Whute Noise vs. Pink Noise - White noise maintains an average power over doubling of frequency - Pink noise: average power decreases with octaves (doubling of frequency) – falling of by 3dB per doubling of frequency Resonators - Damped sinusoidal motion: a free vibration in response to a single input force - Standing waves develop as a result of continuous forced vibrations from external force - Most acoustic events result from forced or driven vibrations - Objects naturally vibrate at their resonant frequency (f ) r - Driving frequencies higher or lower than f arerless efficient - This results in lower vibration amplitude at that frequency Example 1: Complex Sounds - Time domain display: a 1s complex periodic sound - This sound is composed of a 100Hz fundamental frequency (F ) and the first 0 three harmonics of F 0 - All frequency components are integer multiples of F 0 - Frequency domain display illustrates each frequency component and its amplitude Example 2: Complex Sounds - Time domain display: a 1s complex periodic sound - Sound has sam F (100Hz) as precious signal, but the amplitude of the higher harmonics has changed - Decrease in amplitude of the higher harmonic results
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