Goertzel Algorithm - Digital Signal Processing and Applications with the C6713 and C6416 DSK - page 493

Goertzel Algorithm

Goertzel's algorithm performs a DFT using an IIR filter calculation. Compared
to a direct N -point DFT calculation, this algorithm uses half the number of real
multiplications, the same number of real additions, and requires approximately 1/ N
the number of trigonometric evaluations. The biggest advantage of the Goertzel
algorithm over the direct DFT is the reduction of the trigonometric evaluations.
Both the direct method and the Goertzel method are more efficient than the FFT
when a “small” number of spectrum points is required rather than the entire spec-
trum. However, for the entire spectrum, the Goertzel algorithm is an N 2 effort, just
as is the direct DFT.

G.1 DESIGN CONSIDERATIONS

Both the first-order and the second-order Goertzel algorithms are explained in
several topics [1-3] and in Ref. [4]. A discussion of them follows. Since

We

N kN

-

=

j 2 p k

= 1

both sides of the DFT in (6.1) can be multiplied by it, giving

N -

 0

1

() = () Xk W

- kN

xrW

+ kr

(G.1)

N N

r =