Xref: utzoo sci.electronics:18238 comp.dsp:1346 Path: utzoo!news-server.csri.toronto.edu!cs.utexas.edu!wuarchive!sdd.hp.com!think.com!mintaka!bloom-beacon!eru!hagbard!lunic!my!edf From: edf@sm.luth.se (Ove Edfors) Newsgroups: sci.electronics,comp.dsp Subject: Re: A question about the Nyquist theorm Message-ID: <673@my.sm.luth.se> Date: 6 Mar 91 11:28:11 GMT References: <20408@shlump.nac.dec.com> <625@ctycal.UUCP> <11515@pasteur.Berkeley.EDU> Followup-To: sci.electronics Organization: University of Lulea, Sweden Lines: 89 wilf@sce.carleton.ca (Wilf Leblanc) writes: >jbuck@galileo.berkeley.edu (Joe Buck) writes: >>[deleted] >>Example of CD salespeak: pushing oversampling as an advanced technical >>feature. Oversampling is simply inserting zeros between the digital >>samples and thus increasing the sampling rate. It's used because then you >>can use cheaper, less complex analog filters; it reduces the system cost. >>Still, some sales critters think it's an advanced technical extra. >This kills me too. Especially 8x oversampling ! >(I always thought oversampling was used because analog filters usually >have a horrible phase response near the cutoff. However, if you want >to spend enough money, you can get very near linear phase response >with an analog filter. So, you are right). > ... [ stuff deleted ] ... >-- >Wilf LeBlanc Carleton University >Internet: wilf@sce.carleton.ca Systems & Computer Eng. > UUCP: ...!uunet!mitel!cunews!sce!wilf Ottawa, Ont, Canada, K1S 5B6 --- Let me first point out that I'm not very familiar with CD players, so please forgive me if this posting is not compatible with contemprary CD technology. --- The reason for oversampling is, as mentioned above, that analog filters with very sharp cutoff are expensive and/or have a horrible phase response. With oversampling it's possible to use (generaliszed) linear phase discrete time filters prior to the D/A conversion. As a result of this operation one can use much cheaper analog filters on the output. This media is not ideal for graphical illustrations, but I'll try anyway. Let: fs - sampling frequency ( 44 kHz ) Fs - new sampling frequency ( L*44 kHz ) Consider the following amplitude spectrum on a CD: ^ -- --------|-------- -- \ / | \ / \ / | \ / -------+-------------+-------------+---------> -fs/2 fs/2 Reconstruction of this signal require an analog filter with a sharp cutoff frequency at fs/2. After insertion of (L-1) 0's between the samples we get: ^ -- ----- ----- --|-- ----- ----- ----- \ / \ / \ / | \ / \ / \ / \ \ / \ / \ / | \ / \ / \ / \ ---------+--------------+----+----+--------------+---------------> -Fs/2 -fs/2 fs/2 Fs/2 Now ... use a discrete time filter (generalized linear phase) with a sharp cutoff frequency at fs/2 (i.e at fs/Fs - normalized frequency). This operation will give us the following spectrum: (which is a copy of the first one except for the difference that the lobes are furter apart) ^ --|-- / | \ / | \ ---------+--------------+----+----+--------------+---------------> -Fs/2 -fs/2 fs/2 Fs/2 Reconstruction of this signal is much "cheaper" since the analog filter on the output could have a much wider transition region. -------------------------------------------------------------------- Ove Edfors PHONE: Int. +46 920 910 65 Div. of Signal Processing Dom. 0920 - 910 65 University of Lulea FAX: Int. +46 920 720 43 S-951 87 LULEA Dom. 0920 - 720 43 SWEDEN E-MAIL: edf@sm.luth.se --------------------------------------------------------------------