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The Antenna and Band Pass Filter
An antenna is resonant (tuned) to a specific part of the electromagnetic (radio) spectrum providing the optimal collection of the electric field at that specific frequency. This voltage in the form of an alternating sign wave is passed down the coax cable to a band pass filter (BPF) the blocks out (filters out) the unwanted parts of the radio spectrum leaving the wanted signal
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Analogue to Digital Conversion (ADC)
The analogue sign wave is sampled at regular (time) intervals and the voltage value is collected / stored in a range of 0 to 255 (if using 8 bits (couple of nibbles) [e.g. 1010 1010] of computer values)
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The Signal Mixer
The signal mixer takes in the real radio signal received from the antenna and combines that with the local oscillator (which articulates the signal wanted). The mixer then produces a suite of output signals which form the intermediate frequency (baseband) which is passed along to the computer via USB. This is done twice once for the signal in phase "I" and then again for the signal out of phase "Q". This quadrature technique is done to fix the problem of not knowing if the wanted signal is above or below the (wanted) frequency that is articulated by the local oscillator
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The USB SDR Radio
A typical SDR radio will sample the analogue signal voltages post filtering into the digital domain using ADC techniques. The radio will typically do this twice for the signal in phase "I" and out phase "Q" which is then sent to the computer for further processing and demodulation (decoding). After demodulation the encoded signal will be ready for the radio listener
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Under and Over Sampling
Undersampling the ADC would potentially give a wider bandwidth in situations where the ADC is limited by the number of samples (per second) it can handle
Oversampling the ADC can give a larger dynamic range between the signal and noise i.e. it increases the detail (or resolution) of the captured signal
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Nyquist Theorem
The theory that you need twice as much bandwidth to sample a given bandwidth accurately i.e. for 30MHz of bandwidth spectrum capture (at the same time) you need 60MHz (samples per second) of sampling bandwidth