![]() Antennas for those frequencies pick up a lot of AM band RF, overloading the input circuits and creating distortion or false signals inside the receiver. Hams often experience fundamental overload on the 160 meter band (1.8–2.0 MHz) which is adjacent to the AM broadcast (BC) band (550 kHz–1.7 MHz). The AM signal is completely legal but just too strong, disrupting the function of the receiver or overriding the desired programming. The receiver might be a wireless telephone, a scanner, or even a TV or radio receiver. It occurs when a receiving device is functioning entirely properly but unable to reject a strong signal. If you’ve ever lived close to an AM broadcast station, you probably experienced the phenomenon known as fundamental overload. The frequency response of the final filter (with \(f_c=0.1\) and \(b=0.08\)) is shown in Figure 4.» Skip to the Extras Once you start, it’s hard to stop! The values for \(f_c\) and \(b\) in this article were chosen to make the figures as clear as possible. Hence, for a sampling rate of 10 kHz, setting \(b=0.08\) results in a transition bandwidth of about 800 Hz, which means that the filter transitions from letting through frequencies to blocking them over a range of about 800 Hz. As for \(f_c\), the parameter \(b\) should be specified as a fraction of the sampling rate. ![]() Setting \(N=51\) above was reached by setting \(b=0.08\). This is not really required, but an odd-length symmetrical FIR filter has a delay that is an integer number of samples, which makes it easy to compare the filtered signal with the original one. With the additional condition that it is best to make \(N\) odd. To keep things simple, you can use the following approximation of the relation between the transition bandwidth \(b\) and the filter length \(N\), The final task is to incorporate the desired transition bandwidth (or roll-off) of the filter. The central part of a sinc filter with \(f_c=0.1\) is illustrated in Figure 1.įigure 3. For example, if the sampling rate is 10 kHz, then \(f_c=0.1\) will result in the frequencies above 1 kHz being removed. The cutoff frequency should be specified as a fraction of the sampling rate. The impulse response of the sinc filter is defined as The sinc function must be scaled and sampled to create a sequence and turn it into a (digital) filter. The windowed-sinc filter that is described in this article is an example of a Finite Impulse Response ( FIR) filter. And, since multiplication in the frequency domain is equivalent with convolution in the time domain, the sinc filter has exactly the same effect. Multiplying the frequency representation of a signal by a rectangular function can be used to generate the ideal frequency response, since it completely removes the frequencies above the cutoff point. This is because the sinc function is the inverse Fourier transform of the rectangular function. When convolved with an input signal, the sinc filter results in an output signal in which the frequencies up to the cutoff frequency are all included, and the higher frequencies are all blocked. The sinc filter is a scaled version of this that I’ll define below. The sinc function ( normalized, hence the \(\pi\)’s, as is customary in signal processing), is defined as Theoretically, the ideal (i.e., perfect) low-pass filter is the sinc filter. How to create a simple low-pass filter? A low-pass filter is meant to allow low frequencies to pass, but to stop high frequencies. This article is complemented by a Filter Design tool that allows you to create your own custom versions of the example filter that is shown below, and download the resulting filter coefficients. Summary: This article shows how to create a simple low-pass filter, starting from a cutoff frequency \(f_c\) and a transition bandwidth \(b\).
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