Cypress DCT-1D Uživatelská příručka stáhnout pdf (Strana 37)

3.4. A BENCHMARK PROGRAM

Sofar we have presented three ways of computing the 2-D DCT. We compare the

computation complexity of the algorithms:

Algorithm MUL ADD

Eq (3.1) 4096 4032

Eq (3.2) 1024 892

Loefﬂer original 224 416

The post multiplication with c[u] has been left out of the table.

The OR1200 CPU has no ﬂoating point arithmetic, so the sin/cosine factors and

√

in Figure 3.7 must be mapped to integers. We have chosen to multiply with 2

and

rounding to the nearest integer. We have the following correspondences:

Real number Integer

√

2 11585

cos π/16 8035

sin π/16 1598

cos 3π/16 6811

sin 3π/16 4551

√

2 cos 6π/16 4433

√

2 sin 6π/16 10703

The scheme in Figure 3.7 has a serious drawback. The outputs 3 and 5 pass through

two multipliers. There is, however, a modiﬁed version where this ﬂaw has been re-

moved at the price of 1 extra multiplier and 3 extra adders. The last 3 stages on the

lower part of Figure 3.7 is replaced with the computation scheme in Figure 3.8. This

modiﬁcation is not, in our opinion, so easy to ﬁgure out. The interested reader is

therefore directed to the original article, [4].

+ +

Figure 3.8: Loefﬂer’s modiﬁed algorithm. Computation of the odd part with parallel

multiplications.

We conclude that Loefﬂer’s modiﬁed algorithm can be used with integer arith-

metic. After each run all outputs, except 0 and 4, must be arithmetic right shifted 13

steps. The 2-D DCT will be 8 · A[u, v] compared to (3.2), which can be compensated

for in later stages in the JPEG compression algorithm.

1 2 ... 32 33 34 35 36 37 38 39 40 41 42 ... 81 82

Žádné komentáře

Cypress DCT-1D Uživatelská příručka Strana 37