Mus422: Hw4

James Yu Mus422 Homework 4 1) My signal and spectrum:

I estimate the peak to be about 3 bins wide, which is approximately 140.6250 Hz wide.

To estimate the SPL of other peaks, we use the formula given in the text:

Which is derived using Parseval’s theorem. <w^2> in the case of a sine wave is ½. (b) I estimated the peaks and SPL: Peaks 8812.5 4406 890.6 656.25 562.5 421.8

SPL 115.222 121.68 125.66 134 133.4 134.6

The peaks are not exactly at the frequencies we made the sinusoids to be. This is because we are using a DFT, and we will not likely sample the DTFT at the exact spots where the delta functions are.

(c)

(d) I used the triangle spreading function defined as:

10 log10 (F(dz, L_m)) = (-27 + 0.37 * MAX(L_m – 40, 0) * u(dz)) * |dz| where dz = z(f_maskee – f_masker) and L_m is the masker’s SPL and u(z) is the unit step function The masking curve is then defined as: SPL_B = SPL_A – 15dB + 10 log10 (F(dz, L_m))

(e) None of our signals will be masked. Although, in the rest of the frequency spectrum, we see that the artifacts of our limited time DFT will be masked (the lobes of the imperfect delta functions of our sinusoids). The SMR for all the peaks are approximately as follows:

Frequency 440 550 660 880 4400 8800

SMR 20dB 18.54dB 19.8dB 21.8dB 31.4dB 35dB

Bits Needed 4 4 4 4 6 6

(f) For the hanning window, I get the following mask model:

We see that the rejection of the Hanning window is less. Therefore, more of the spectrum is potentially unmasked. However, in this particular case, only artifacts from the DFT are unmasked (which we know aren’t true signals). But for a real world signal, more of the signal will be unmasked. The SMR for all the peaks are approximately as follows:

Frequency 440 550 660 880 4400 8800

SMR 17.18dB 20dB 21dB 22dB 30.5dB 34.1dB

Bits Needed 4 4 4 4 6 6

(g) Here I graphed my masking model, along with the minimum masking in each critical band.

Band

Minimum Mask

Peaks

Peak SPL

SMR

Bits Needed

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

13.8705 27.4152 51.0559 59.9743 59.5854 55.7996 48.4321 36.105 25.0329 10.5878 1.0374 0.0922 -1.6546 -3.4206 -4.9077 -4.9758 20.2607 21.2243 6.0862 2.7544 9.3013 13.3684 17.9116 58.3591

17.5

3.6295

36.185

8.7698

43.7925

-7.2634

58.8877

-1.0866

440 Hz

83.4

23.8146

4

550 Hz

82.2

26.4004

5

660 Hz

82.8

34.3679

6

880 Hz

74.5

38.395

7

49.4105

24.3776

35.2918

24.704

29.9561

28.9187

23.6739

23.5817

19.0013

20.6559

15.2899

18.7105

12.2

17.1077

10.7942

15.77

7.9484

-12.3123

14.5982

-6.6261

70.5

64.4138

38

35.2456

18

8.6987

64

50.6316

4400 Hz

8800 Hz

18

0.0884

-13

-71.3591

11

9