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=== Basic Characteristics === | === Basic Characteristics === | ||
| − | When designing filters, it is important to understand where the desired/important information is contained in the signal of interest. In a time-domain important signal, desired information is contained in the amplitude changes when an event occurs, for example, intensity of sunlight on a forest floor over time. Meanwhile in the frequency-domain, one is primarily concerned with the | + | When designing filters, it is important to understand where the desired/important information is contained in the signal of interest. In a time-domain important signal, desired information is contained in the amplitude changes when an event occurs, for example, intensity of sunlight on a forest floor over time. Meanwhile in the frequency-domain, one is primarily concerned with the information contained in a signal's component sinusoids. |
| − | The step response and the frequency response of a filter or system of filters provides a way to understand how a filter will affect our signal of interest. The step response is the integrated impulse response and | + | The step response and the frequency response of a filter or system of filters provides a way to understand how a filter will affect our signal of interest. The step response is the integrated impulse response and will show how the filter will affect the signal in the time-domain. On the other hand, the frequency response will show how the info will be changed in the frequency domain. |
Some additional points to consider in digital filters for time-domain applications are (1) rise-time, (2) overshoot, and (3) phase changes and for frequency-domain applications are (1) passband ripple, (2) stopband attenuation, and (3) roll-off speed. | Some additional points to consider in digital filters for time-domain applications are (1) rise-time, (2) overshoot, and (3) phase changes and for frequency-domain applications are (1) passband ripple, (2) stopband attenuation, and (3) roll-off speed. | ||
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</gallery> | </gallery> | ||
| − | === Finite Impulse Response === | + | === Finite Impulse Response and Infinite Impulse Response === |
| − | Finite impulse response filters | + | Finite impulse response filters (FIR) convolve the impulse response of a system with the signal(s) of interest. The impulse response finite and also referred to as a filter kernel. Thanks to their limited duration, they can be convolved with signals of interest for good but orders of magnitude slower performance than IIR filters. |
| − | + | Examples of FIR filers are the Moving Average Filter, Hamming, Blackman, and the Windowed Sinc. | |
| − | + | Infinite impulse response filters (IIR) rely on both system inputs and system outputs to produce new outputs. Their reliance on previous outputs means that they are implemented in a recursive fashion and are also referred to as recursive filters. In the frequency domain | |
| − | == | + | Examples of IIR filters are the Chebyshev, Butterworth, and Bessel. |
| + | |||
| + | Additional information for both FIR and IIR filters can be found on previous slectures concerning the Z-Transform. | ||
| + | |||
| + | === Low Pass Filters === | ||
Revision as of 15:33, 7 December 2017
Contents
Digital Filters: An Introduction
Objectives:
Digital filters are used for two main purposes below. A big advantage for digital filters over analog ones is that digital filters can satisfy criteria for filters far better than analog ones. This slecture hopes to share characteristics important to digital filter use and design in addition to how concepts learned in ECE 438 apply to actual filter design.
1. Separation of signals that have been combined
2. Restoration of signals that have been distorted in some way
Basic Characteristics
When designing filters, it is important to understand where the desired/important information is contained in the signal of interest. In a time-domain important signal, desired information is contained in the amplitude changes when an event occurs, for example, intensity of sunlight on a forest floor over time. Meanwhile in the frequency-domain, one is primarily concerned with the information contained in a signal's component sinusoids.
The step response and the frequency response of a filter or system of filters provides a way to understand how a filter will affect our signal of interest. The step response is the integrated impulse response and will show how the filter will affect the signal in the time-domain. On the other hand, the frequency response will show how the info will be changed in the frequency domain.
Some additional points to consider in digital filters for time-domain applications are (1) rise-time, (2) overshoot, and (3) phase changes and for frequency-domain applications are (1) passband ripple, (2) stopband attenuation, and (3) roll-off speed.
Impulse, step, and frequency responses.
Finite Impulse Response and Infinite Impulse Response
Finite impulse response filters (FIR) convolve the impulse response of a system with the signal(s) of interest. The impulse response finite and also referred to as a filter kernel. Thanks to their limited duration, they can be convolved with signals of interest for good but orders of magnitude slower performance than IIR filters.
Examples of FIR filers are the Moving Average Filter, Hamming, Blackman, and the Windowed Sinc.
Infinite impulse response filters (IIR) rely on both system inputs and system outputs to produce new outputs. Their reliance on previous outputs means that they are implemented in a recursive fashion and are also referred to as recursive filters. In the frequency domain
Examples of IIR filters are the Chebyshev, Butterworth, and Bessel.
Additional information for both FIR and IIR filters can be found on previous slectures concerning the Z-Transform.
