The FFT analyzer consists of a number of components, each of which is necessary for frequency analysis. First, signals must pass through attenuators or gain stages to adjust the amplitude of the signal to match the input range so as to maximize the resolution of the signal. The signal is passed through an anti-aliasing filter, which we discuss in detail later. Next, a sampler takes discrete points of the analog waveform at a given frequency. This is followed by an analog-to-digital converter (ADC), which converts the samples into digital data. The data is transformed to the frequency domain using the FFT algorithm. The analyzer can use dedicated DSP circuitry to perform the FFT, or the data can be transferred to a PC where the FFT is calculated using software.
The rate at which points are taken by the sampler is a very important parameter of the FFT analyzer. In order for an analog waveform to be represented correctly with discrete values, it must be sampled at a sufficiently high rate. Otherwise the analyzer will interpret the input as a signal of frequency lower than the actual value. According to the sampling theorem, a signal must be sampled at a rate of twice the highest frequency component (the Nyquist rate). Any component whose frequency is higher than the Nyquist rate will appear in the measurement as a lower frequency component. This phenomenon is called aliasing. To avoid aliasing, an analog low-pass filter is placed at the input before the sampler. The low-pass filter determines the highest frequency of the FFT analyzer. Because the rate at which signals can be represented without error is one half the maximum sampling rate, signals are often cut off at a lower frequency to provide sampling rates greater than twice the maximum frequency components. Typically the cutoff of the low-pass filter is 2.5 times less than the maximum sampling rate of the analyzer. This determines the maximum frequency component.
The FFT algorithm is calculated from time records. Each record contains a finite number of discrete points. The FFT converts these time domain points into a finite number of frequency domain points. The frequency domain representation is symmetric about the 0 Hz frequency point. Only the upper half of the transform, which pertains to 0 Hz and above, is kept. Thus, only a certain number of frequencies can be analyzed. The frequency resolution, or spacing between the bins, must be such that the acquired frequencies are represented properly. In order to increase the frequency resolution the number of samples must increase. This is because the frequency resolution is inversely proportional to the length of the time record.
The transformed frequency domain data has an initial frequency value of 0 Hz and extends to 1/2 the sampling frequency, the maximum range of the FFT. If the number of samples is kept equal as the frequency range increases, the spacing between frequency bins increases. Thus the frequency resolution decreases. An alternative is to increase the number of samples acquired. However, increasing the number of samples requires a greater computational burden. In order to decrease the sampling rate without causing aliasing, a digital filter may be inserted between the ADC and the FFT to remove frequency components that are above twice the current sampling rate.
Because of the previously mentioned conditions, the measurement of higher frequencies with good resolution becomes quite difficult. However, by inserting a digital mixer between the ADC and the digital filter, a discrete sine wave can be multiplied to the incoming signal and effectively decrease the signal frequency. By reducing the signal frequency, the FFT can be performed on a range that has an offset from 0 Hz. This range is called band selectable analysis or zoom FFT analysis.
Whether an FFT analyzer is considered real time or not is determined by the computing time of the FFT. If the time to compute the FFT was faster than the rate at which the data was sampled, then an FFT could be performed for each point. However, this would require computational power beyond that of most instruments. A shortcut is to take a certain number of samples and transfer them to an intermediate buffer. The FFT takes the data from this buffer to perform its operation. If the FFT is computed before the next time record is placed in the buffer, then the analyzer is running in real time.
Because the number of samples in the time record is inversely proportional to the frequency span, it takes less time to compute the FFT for larger frequency spans. The point at which the frequency span time record equals the time it takes to compute the FFT is called the real-time bandwidth. To increase the speed at which the analyzer performs the FFT, dedicated DSP circuitry is placed on the instrument. Stand-alone and computer-based instruments use this method. Another method used by computer-based instruments is to use a digitizer to acquire the data, then transfer the data to a memory buffer. The FFT is then performed on the host PC in software.