STFT Filter Bank

Each channel of an STFT filter bank implements the processing shown in Fig.9.4. The same processing is shown in the frequency domain in Fig.9.5. Note that the window transform is complex-conjugated because the window is flipped in the time domain, i.e., when is real [243].

These channels are then arranged in parallel to form a filter bank, as shown in Fig.9.3. In practice, we need to know under what conditions the channel filters will yield perfect reconstruction when the channel signals are remodulated and summed. (A sufficient condition for the sliding STFT is that the channel frequency responses overlap-add to a constant over the unit circle in the frequency domain.) Furthermore, since the channel signals are heavily oversampled, particularly when the chosen window has low side-lobe levels, we would like to be able to downsample the channel signals without loss of information. It is indeed possible to downsample the channel signals while retaining the perfect reconstruction property, as we will see in §9.8.1.

---

Subsections

• Computational Examples in Matlab

---

Order a Hardcopy of Spectral Audio Signal Processing

Previous: FBS and Perfect Reconstruction
Next: Computational Examples in Matlab

---

written by Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.