Perceptual Audio Coding Hw4

Music 422/ EE 367C Winter 2006/2007 Assignment #4 Due February 9, 2007 1) Masking Curves: In this exercise you will develop the masking curve for a test signal. We will return to this test signal in the next assignment and use the masking curve to guide bit allocation for this signal. a) Use an FFT to map a 1 kHz sine wave with amplitude equal to 1.0 into the frequency domain. Use a sample rate of 48 kHz and a block length of N = 1024. You may use a sine (or Hanning) window. How wide is the peak? If we define this signal as having an SPL of 96 dB, how can you estimate the SPL of other peaks you see in a test signal analyzed with the same FFT? (Hint: Parseval’s Theorem for the DFT is

< x[n ] 2 > ≡

1 N

∑ x[n ] n

2

=

1 N2

∑ X[k ]

2

k

Also, the sine and the Hanning window reduce the power spectral density by a factor of 2 and 8/3 respectively, and half of the power is in the negative frequency content. See also pages 227-229 of the textbook.) b) Use the same FFT to analyze the following signal:

x[n] = A0 cos(2π 440n / Fs ) + A1 cos(2π 550n / Fs ) + A2 cos(2π 660n / Fs ) + A3 cos(2π 880n / Fs ) + A4 cos(2π 4400n / Fs ) + A5 cos(2π 8800n / Fs ) where A0 = 0.45, A1 = 0.15, A2 = 0.15, A3 = 0.08, A4 = 0.06, A5 = 0.04, and FS is the sample rate of 48 kHz. Using the FFT results, identify and estimate the SPLs of the peaks in the signal. How do these results compare with what you know the answer to be based on the signal definition? c) Apply the threshold in quiet to this spectrum. Create a graph comparing the test signal’s frequency spectrum (measured in dB) with the threshold in quiet. d) Define a masking model and specify its parameters, namely the spreading function and the downshift ∆. (Recall that masking models are simpler to define in the Bark scale.) Use the masking model to define masking curves for the test signal. Create the masked curve for the signal (i.e. the combination of the signal components masking curves and the threshold in quiet). Prepare a graph comparing the test signal’s frequency spectrum (measured in dB) with the masked curve. e) Are any of your signal peaks going to be masked? How about the rest of the frequency spectrum? What is the signal to mask ratio (SMR) of any of the unmasked signal peaks? Assuming 6 dB per bit, how many bits of resolution are needed for each unmasked signal peak? f) (Extra Credit) What are the differences in the answers to the questions in e) between a sinewindowed and the Hanning-windowed signal? g) Group the FFT frequency lines into the 25 critical bands. What is the lowest level of the masking curve in each critical band? If you assume that this level of masking applies in each critical band, create a new graph comparing the test signal’s frequency spectrum with the level of masking. What will be masked? How many bits of resolution are needed for each unmasked signal peak? What is the maximum signal-to-mask ratio (SMR) for each critical band?

2) Reading Assignment: Chapters 8 and 9 from the textbook, M. Bosi and R. E. Goldberg, “Introduction to Digital Audio Coding and Standards”, KAP 2003.