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U. Glaeser

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FIGURE 27.19 Overlapped, power complementary MDCT windows.<br />

is quite flexible. A long block can be split into a shorter block. Figure 27.19 presents possible transitions<br />

MDCT windows between long and short block modes. The length of the block depends on stationarity<br />

of the input signal.<br />

The respective inverse discrete cosine transform (IMDCT) is defined as<br />

The input signal is recovered with an overlap add operation<br />

which cancels the time-domain aliasing.<br />

FIR Filters<br />

© 2002 by CRC Press LLC<br />

(27.40b)<br />

(27.40c)<br />

Basic operation in digital audio signal processing is frequency selective filtering. It can be realized in<br />

frequency domain, e.g., using FFT and in time domain using finite impulse response (FIR) and infinite<br />

impulse response (IIR) filters. Mostly FIR filters are used because they are always stable and can be easily<br />

designed with perfect linear phase characteristic.<br />

Assuming an ideal filter frequency response given by<br />

where<br />

N/2−1<br />

0.8<br />

0.6<br />

0.4<br />

0.2<br />

the respective FIR filter impulse response is<br />

1<br />

0<br />

0 50 100 150<br />

yl( n)<br />

w( n)<br />

N<br />

π<br />

--- Xl( k)<br />

------ 2n 1<br />

4<br />

2N<br />

N<br />

= ⎛ ⎛ + + ---- ⎞( 2k + 1)<br />

⎞<br />

∑ cos<br />

for n = 0, 1,…, N – 1<br />

⎝ ⎝ 2 ⎠ ⎠<br />

k=0<br />

x˜ l( n)<br />

yl−1 n N ⎛ + ---- ⎞ + y<br />

⎝ 2 ⎠ l( n)<br />

for n 0, 1,…, N<br />

= = --- – 1<br />

2<br />

h( n)<br />

+∞<br />

∑<br />

– ωn<br />

H e jω<br />

( ) h( n)e<br />

j<br />

=<br />

n=−∞<br />

1<br />

2π<br />

----- Hd e jω<br />

+∞<br />

= ∫<br />

−∞<br />

( )e jωn dω<br />

hFIR( n)<br />

=<br />

wN( n)h(<br />

n)<br />

(27.41)<br />

(27.42)<br />

(27.43)

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