> for linear interpolation, if you are a delayed by 3.5 samples and you keep that delay constant, the transfer function is > > H(z) = (1/2)*(1 + z^-1)*z^-3 > >that filter goes to -inf dB as omega gets closer to pi.
Note that this holds for symmetric fractional delay filter of any odd order (i.e., Lagrange interpolation filter, windowed sinc, etc). It's not an artifact of the simple linear approach, it's a feature of the symmetric, finite nature of the fractional interpolator. Since there are good reasons for the symmetry constraint, we are left to trade off oversampling and filter order/design to get the final passband as flat as we need. My view is that if you are serious about maintaining fidelity across the full bandwidth, you need to oversample by at least 2x. That way you can fit the transition band of your interpolation filter above the signal band. In applications where you are less concerned about full bandwidth fidelity, oversampling isn't required. Some argue that 48kHz sample rate is already effectively oversampled for lots of natural recordings, for example. If it's already at 96kHz or higher I would not bother oversampling further. Also this is recommended reading for this thread: https://ccrma.stanford.edu/~jos/Interpolation/ E On Tue, Aug 18, 2015 at 1:45 PM, Tom Duffy <tdu...@tascam.com> wrote: > In order to reconstruct that sinusoid, you'll need a filter with > an infinitely steep transition band. > You've demonstrated that SR/2 aliases to 0Hz, i.e. DC. > That digital stream of samples is not reconstructable. > > On 8/18/2015 1:28 PM, Peter S wrote: > > That's false. 1, -1, 1, -1, 1, -1 ... is a proper bandlimited signal, >> and contains no aliasing. That's the maximal allowed frequency without >> any aliasing. It is a bandlimited Nyquist frequency square wave (which >> is equivalent to a Nyquist frequency sine wave). From that, you can >> reconstruct a perfect alias-free sinusoid of frequency SR/2. >> > > NOTICE: This electronic mail message and its contents, including any > attachments hereto (collectively, "this e-mail"), is hereby designated as > "confidential and proprietary." This e-mail may be viewed and used only by > the person to whom it has been sent and his/her employer solely for the > express purpose for which it has been disclosed and only in accordance with > any confidentiality or non-disclosure (or similar) agreement between TEAC > Corporation or its affiliates and said employer, and may not be disclosed > to any other person or entity. > > > > > _______________________________________________ > music-dsp mailing list > music-dsp@music.columbia.edu > https://lists.columbia.edu/mailman/listinfo/music-dsp >
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