I am new here and a beginner with SDR & FFT. For antenna pattern measurements, a flying probe antenna is to be used to sample the electromagnetic near-field in front of an antenna. A lightweight spectrum analyser (SA) is to be used to provide a continuous stream of IQ signals. At defined times, this stream shall be sliced into minimum sample durations centred on the defined times to enable FFTs obtaining amplitude and phase values for several known measurement frequencies radiated by the DUT. The front end of the SA consists of a zero IF receiver followed by a digital downconverter providing the IQ stream. The intention is to perform FFTs for at least one full cycle of the measurement frequency or a multiple of that for each measurement frequency. I am a bit puzzled as to how to determine the length of one complete cycle, firstly for the centre frequency which is DC or 0 Hz resulting in an infinitely long sample duration, or for frequencies very close to the centre frequency resulting in relatively long sample durations. E.g: Measuring navigation signals of an ILS glide path of +/-90 and +/-150 Hz at 330 MHz would require a sample duration of 11.1 ms or 6.7 ms, which seems rather long. The sampling rate is 180 kHz. My question is whether the minimum one cycle requirement for the FFT is still relevant in this scenario and, if so, are there any ways to overcome this? Thanks for any advice.
1 Answers
Without considering the effects of windowing (shaping) the captured waveform prior to taking the FFT, the resolution bandwidth of any one FFT bin including the DC bin is $f_s/N$ Hz, where $f_s$ is the sampling rate and $N$ is the number of samples. This is the equivalent bandwidth that a brickwall filter centered on the bin frequency to produce the same noise power out under the condition of white noise at the input. The actual filter magnitude response of a single bin is a Sinc function with the first null spaced 1 bin away (the area under a Sinc with the main lobe as 2 bins wide is equivalent to a rectangular shape one bin wide, hence the relationship of resolution bandwidth under white noise conditions). This then provides an additional explanation into spectral leakage: how other bins respond to a single tone close to one bin. I explain how the FFT is a bank of filters and the relationship between the captured signal duration and the resolution bandwidth for each of these "filters" in DSP.SE Post 82998.
So with that the choice of measurement duration affects the resolution bandwidth of the measurement. The calculation above results in the general expression which can be applied to all signal captures analog or digital $RBW = 1/T$ Hz where $T$ is the measurement duration in seconds. What this means is if we want to resolve to closely spaced frequencies (that are each similar in power level) as two distinct tones, a longer measurement duration may be necessary.
When windows are applied (other than the rectangular window we naturally get when we select an arbitrary block of data), the resolution bandwidth is increased at the benefit of much lower sidelobes than we get with a Sinc function: The Sinc function as the Fourier Transform of a rectangular window has the narrowest mainlobe but highest sidelobes compared to all the other common windows used for FFT processing (such as Kaiser, Hamming, Blackman etc).
Specific to Zero-IF receivers: There will be an inevitable DC offset from the analog portion of the design including the ADC itself, that may be blocked with a DC nulling filter (equivalent to a series cap)- if present, this will have a high pass response affecting any of the measurements near DC. If not present, the DC offset introduced in the analog will act as an interference tone to any measurements there and will vary (slowly) over time.
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