Download low-pass filter

 High-Pass
Filter.
 Low-Pass Filter.
 Band-Pass Filter.
 Band-Stop Filter.
 Finite Impulse Response Filter (FIR).
 Infinite Impulse Response Filter (IIR).
 References.
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A high-pass filter (HPF) is a device that passes high frequencies and attenuates
frequencies lower than its cutoff frequency. A high-pass filter is usually modeled as a
linear time-invariant system. It is sometimes called a low-cut filter or bass-cut filter.
High-pass filters have many uses, such as blocking DC from circuitry sensitive to nonzero average voltages or RF devices. They can also be used in conjunction with a lowpass-filter to make a band-pass filter. The actual amount of attenuation for each
frequency is a design parameter of the filter.
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The simple first-order electronic high-pass(passive filter) filter is implemented by
placing an input voltage across the series combination of a capacitor and a resistor
using the voltage across the resistor as an output. The product of the resistance and
capacitance (R×C) is the time constant (τ); it is inversely proportional to the cutoff
frequency fc, at which the output power is half the input power.
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An active electronic implementation of a first-order high-pass filter using an
operational amplifier. In this case, the filter has a pass-band gain of -R2/R1 and has a
corner frequency.
Because this filter is active, it may have non-unity pass-band gain. That is, highfrequency signals are inverted and amplified by R2/R1.
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A low-pass filter is an electronic filter that passes low-frequency signals but
attenuates signals with frequencies higher than the cutoff frequency. It is sometimes
called a high-cut filter, or treble cut filter when used in audio applications. A low-pass
filter is the opposite of a high-pass filter. A band-pass filter is a combination of a lowpass and a high-pass.
Low-pass filters exist in many different forms, including electronic circuits, such as
anti-aliasing filters for conditioning signals prior to analog-to-digital conversion. Lowpass filters provide a smoother form of a signal, removing the short-term fluctuations,
and leaving the longer-term trend.
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One simple electrical circuit that will serve as a low-pass filter consists of a resistor in
series with a load, and a capacitor in parallel with the load. The capacitor exhibits
reactance, and blocks low-frequency signals, causing them to go through the load
instead. At higher frequencies the reactance drops, and the capacitor effectively
functions as a short circuit.
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Another type of electrical circuit is an active low-pass filter. In the operational amplifier
circuit shown in the figure:
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The gain in the pass-band is −R2/R1, and the stop-band drops off at −6 dB per octave
as it is a first-order filter
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A band-pass filter is a device that passes frequencies within a certain range and
rejects (attenuates) frequencies outside that range.
An example of an analogue electronic band-pass filter is an RLC circuit (a resistor–
inductor–capacitor circuit). These filters can also be created by combining a lowpass filter with a high-pass filter.
The bandwidth of the filter is simply the difference between the upper and lower
cutoff frequencies.
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A band-stop filter or band-rejection filter is a filter that passes most frequencies
unaltered, but attenuates those in a specific range to very low levels. It is the
opposite of a band-pass filter.
Its also a combination of a LPF and HPF.
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A finite impulse response (FIR) filter is a type of a signal processing filter
whose impulse response (or response to any finite length input) is of finite
duration, because it settles to zero in finite time.
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This is in contrast to infinite impulse response (IIR) filters, which have
internal feedback and may continue to respond indefinitely.
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The impulse response of an Nth-order discrete-time FIR filter lasts for N+1
samples, and then dies to zero.
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FIR filters can be discrete-time or continuous-time, and digital or analog.
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The output y of a linear time invariant system is determined by convolving its input
signal x with its impulse response b.
For a discrete-time FIR filter, the output is a weighted sum of the current and a finite
number of previous values of the input. The operation is described by the following
equation, which defines the output sequence y[n] in terms of its input sequence x[n].
An FIR filter has a number of useful properties:
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Require no feedback. This means that any rounding errors are not
compounded by summed iterations.
Are inherently stable. This is due to the fact that, because there is no
required feedback.
They can easily be designed to have linear phase by making the
coefficient sequence symmetric;
The main disadvantage of FIR filters is that considerably more
computation power in a general purpose processor is required
compared to an IIR filter with similar. However many digital signal
processors provide specialized hardware features to make FIR filters
approximately as efficient as IIR for many applications.
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Infinite impulse response (IIR) is a property of signal processing systems.
Systems with this property are known as IIR systems or, when dealing with
filter systems, as IIR filters. IIR systems have an impulse response function
that is non-zero over an infinite length of time.
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The simplest analog IIR filter is an RC filter made up of a single resistor (R)
feeding into a node shared with a single capacitor (C). This filter has an
exponential impulse response characterized by an RC time constant.
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IIR filters may be implemented as either analog or digital filters.
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Design of digital IIR filters is heavily dependent on that of their analog
counterparts because there are plenty of resources, works and
straightforward design methods concerning analog feedback filter design
while there are hardly any for digital IIR filters.
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The most commonly used IIR filter design method uses reference
analog prototype filter.
The filter design process starts with specifications and requirements
of the desirable IIR filter.
A type of reference analog prototype filter to be used is specified
according to the specifications and after that everything is ready for
analog prototype filter design.
The next step in the design process is scaling of the frequency range
of analog prototype filter into desirable frequency range. This is how
an analog prototype filter is converted into an analog filter.
The last step in the digital IIR filter design process. It is conversion
from analog to digital filter. The most popular and most commonly
used converting method is bilinear transformation method.
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Concept: It can also be called zeros and poles mapping.
Basically, it’s converting the desired signal from continuous-time
filter to discrete-time filter.
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Digital IIR filters are designed using analog filters. After the
frequency scaling and transformation into desirable type of filter
has been performed. It’s necessary to transform the resulting
analog filter into a digital one. It’s done by transforming the analog
filter transfer function into a digital one.
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The transformation is supposed to be:
1.
2.
Faithfully approximate the frequency response of analog filter. And
Provide that the resulting digital filter is guaranteed to be stable
Butterworth Analog Filter
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It’s a basic low-pass filter that can be modified to give low-pass,
High-pass, band-stop, band-pass Functionality.
Characterized by 3dB attenuation.
It has a flat magnitude.
Chebyshev Analog filter
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It has the least oscillation in the Frequency response in the entire
pass-band.
It is characterized by the equal ripple in the pass-band and stopband.
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A high order IIF filter consists of multiple second order multiplied all together resulting a
high order IIR filter
H(z)=H1(z)*H2(z)*Hn(z) Where n is the order of the filter.
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ADC quantizing noise, results from representing
the samples of x(n) by small number of bits.
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Overflow errors, which result from arithmetic
operations and save the output in a limited
register length.
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to reduce errors in IIR Filter is by break H(z)
into smaller first and second order blocks, the it
should be connected in cascade or in parallel.
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Telecommunication- in Transmitters as antialiasing filter. And, in Receivers anti-imaging
filter.
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Digital Telephony-digital dual tone multifrequency touch-tone receiver.
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Clock recover in Data communications.
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www.wikipedia.com
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Analog and digital signal processing by John
Kronenburger and John Sebeson.