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I thinking about FM and AM. Theoretically the carrier frequency is perfectly match the demodulation frequency. But what happens if there is a mismatch?
I think using AM the frequency of the base-band analog output will be pitched low/high depends on higher/lower demodulation frequency respectively. Am I right?
But what happens using FM?
With both AM and FM, there are sidebands on both sides of the carrier.
With AM there is a simple relationship between the sideband offset frequency and the modulation frequency but with FM the relationship is less straightforward. With both types of modulation the edges of the signal spectrum with be attenuated by the IF filter if there is a frequency error.
AM usually uses envelope demodulation and is quite tolerant of frequency errors. The pitch of the demodulated signal comes from the difference between the carrier and sideband frequencies, which remains constant as the error increases, so no pitch change. There is only moderate distortion with just the carrier and one sideband with AM but as soon as the carrier is filtered out, the envelope is destroyed and there is gross distortion.
Try listening to a single sideband signal with an envelope detector. With FM there will be distortion if some parts of the signal are lost. You can experiment with a broadcast band receiver but bear in mind that the filters are usually not very sharp.
With AM, only the envelope of the signal inside the filter passband matters. As the signal moves out, this gives light distortions, until the signal's center frequency passes the filter's transition band, then signal level decreases rapidly while distortions increase. Since the mean signal level is the "zero" point for the modulation signal, this means that noise will increase, usually until it hits a cutoff.
For FM, this causes a shift in the zero point of the modulation signal, so a DC offset. A high pass filter in the audio path filters out this signal. As with AM, as you move further away, the signal gets distorted by the transition band of the tuning filter.
FM stereo is a bit of a special case as it uses a pilot tone to allow the receivers to locate the difference signal. If the receiver tuning moved downwards, the pilot tone will drop out of the filter passband, and the receiver falls back to mono; when tuning upwards, the receiver will demodulate the pilot tone instead, which is constant frequency, so it will demodulate to a DC signal that is then filtered out.
For FM: If the carrier frequency fc does not exactly meet the local osciallator frequency lc in the demodulator stage you will get frequencies resulting from product: fc*lc. If the missmatch is large enough the bandpass filter filters out the "undesired" products and you will receive no information (e.g. will not hear that particular radio channel).
The best AM (and NTSC analog TV is analog AM) detector uses phase-locked-carrier product-detector. Allows tighter filtering and thus better transient/music/video signal recovery. The Motorola MC44301 does this.
The best FM detector may be the Marantz 10B, a vacuum tube FM stereo music receiver, where a front-panel 2" oscilloscope display provides realtime monitoring of multipathing and mis-aligned IF filters and mis-aligned transmitter-receiver carriers. The RF FM is downconverted and amplified and heavily and sharply filtered, and zero-crossings are detected and converted into fast-edge digital pulses. These pulses carry the FM information, and drive a fixed pulse-width (monostable) circuit, the output of which is heavily filtered (Marantz does not say how many poles are used) to provide the recovered information.
Note the presence of frequency-error results in DC output, and a high-pass-filter blocks this. Also note the presence of phase-noise causes slight timing fluctuation of the information-carrying zero-crossings; all oscillators have some phase-noise (aka jitter); if broadband, the human ear is not bothered; if tonal as from 60/120Hz power supply effects, the listener will complain.
However, I've seen circuits for some of the GSM cellphones; these used zero-IF detection, where the receiver oscillator is "on" the Transmitter frequency but with slight frequency error and unknown phase error.
To properly handle these errors, the zero-IF signal (separated into Inphase and Quadrature parts) is digitized and the packet (GSM cellphones use 577 packets per second) training sequence is processed to extract the phase-rotation during that mid-packet known-bit-pattern interval. By examining phase-rotation, and then cancelling the phase-rotation, an adequately phase-constant signal (digital, at this point) is available for data-eye matching against the four phase-patterns allowed in GSM.
