Fast Hartley Transform - Digital Signal Processing and Applications with the C6713 and C6416 DSK - page 492

2 n

N

p p n

C n = cos = cos

8

2 n

N

p p n

S n = sin = sin

8

with N = 16, X (1) can be obtained from Figure F.2:

() =

X 1 3 414 . + 3 414 . C 1 - 1 414 1 . S = 3 414 . + 3 154 . - 0 541 . = 6 027 .

as in Figure F.2. Equation (F.18) can be used to verify X (1) = 1 - j 5.028, as obtained

using the FFT in Example 6.2. Note that, for example,

() =- ( ) + ( )

X 15 1 414 . + - 1 414 . C 15 3 414 15 . S

=- 1 414 . - 1 306 . - 1 306 .

=- 4 0269 .

as shown in Figure 6.15.

REFERENCES

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pp. 1010-1018.

2. R. N. Bracewell, Assessing the Hartley transform, IEEE Transactions on Acoustics,

Speech, and Signal Processing , Vol. ASSP-38, 1990, pp. 2174-2176.

3. R. N. Bracewell, The Hartley Transform , Oxford University Press, New York, 1986.

4. R. N. Bracewell, The Fourier Transform and its Applications , McGraw Hill, New York,

2000.

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transform algorithms, IEEE Transactions on Acoustics, Speech, and Signal Processing ,
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8. A. Zakhor and A. V. Oppenheim, Quantization errors in the computation of the discrete

Hartley transform, IEEE Transactions on Acoustics, Speech, and Signal Processing , Vol.
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