[mus422] Hw3 solutions

[Marina Bosi]

Hello everyone,

 

Craig, thanks for sending the solution for hw #3.    

 

Everyone, please ***update/correct*** the solution so that the
normalization reflects the summation over frequency lines neighboring the
peaks.   

 

By just including the power in the peak line one gets normalization
factors that are too small.  (For example, Craig gets ~0.41 = (2/pi)^2 for
sine window instead of 1/2.)

 

Enclosed is a small demo program to show this for the case of
sine-windowed DFT.  Here is its output:

 

 

Normalization Example: (2/N*DFT of sine-windowed unit-amplitude sinusoid)

 

 

Spectral Peak:  0.636619834785  (Approx. 2/pi =  0.636619772368  as noted
by Craig)

 

Spectral Peak +  1  neighbor(s) on each side: 

[ 0.21220653  0.63661983  0.21220653]

 

 

Sum over peak:  0.405284814042  (Approx. (2/pi)^2 =  0.405284734569  as
noted by Craig)

 

Sum over Broadened peak:  0.495348035409  (Approx. <w^2> = 1/2 as in book
p. 229 for sine window)

 

Marina Bosi

Consulting Professor, Department of Music

Stanford University

 

Computer Center for Research in Music and Acoustics

The Knoll,  660 Lomita Court

Stanford, California 94305-8180, USA

http://ccrma.stanford.edu

mbosi at stanford.edu

 

-----Original Message-----
From: 422-bounces at ccrma.Stanford.EDU
[mailto:422-bounces at ccrma.Stanford.EDU] On Behalf Of Craig Sapp
Sent: Friday, March 05, 2010 8:54 AM
To: 422 at ccrma.Stanford.EDU
Subject: [mus422] Hw3 solutions

 

Hello Music 422 class,

 

Attached are solutions to HW3 giving illustrations of the 1 kHz

sinewave peak aligned in SPL between the MDCT and the DFT (plot 4 on

page 2 illustrates the 1/2 bin shift between the two transforms),

including Kaiser-Bessel Derived windows using alpha of 1 and 4.  Also

on page 3 are a pair of functions which can be used to calculate the

reference amplitude for a given window/transform/transform size

without the need to keep track of normalization factors in order to

display the transform with dB_spl.

 

-=+Craig

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