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**FILTERS Presented by: Mohammed Alani Supervised By: Dr. Nazila Safavi**

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**Contents 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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High-Pass filter 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 non-zero average voltages or RF devices. They can also be used in conjunction with a low-pass-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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HPF/Implementation 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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HPF/Implementation 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, high-frequency signals are inverted and amplified by R2/R1.

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Low-Pass Filter 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 low-pass 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. Low-pass filters provide a smoother form of a signal, removing the short-term fluctuations, and leaving the longer-term trend.

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LPF/Implementation 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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LPF/Implementation Another type of electrical circuit is an active low-pass filter. In the operational amplifier circuit shown in the figure: 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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Band-Pass Filter 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 low-pass 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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Band-Stop Filter 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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**Finite Impulse Response Filter(FIR)**

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. This is in contrast to infinite impulse response (IIR) filters, which have internal feedback and may continue to respond indefinitely. The impulse response of an Nth-order discrete-time FIR filter lasts for N+1 samples, and then dies to zero. FIR filters can be discrete-time or continuous-time, and digital or analog.

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**Finite Impulse Response Filter(FIR)**

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].

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**Finite Impulse Response Filter(FIR)**

An FIR filter has a number of useful properties: 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 Filter(IIR)**

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. 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. IIR filters may be implemented as either analog or digital filters. 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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**IIR Filter/Poles & Zeros Placement**

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IIR filter/Design 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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**IIR/Bilinear Z transformation (BTZ)**

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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IIR Filter/BZT 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. The transformation is supposed to be: Faithfully approximate the frequency response of analog filter. And Provide that the resulting digital filter is guaranteed to be stable

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**Filter that can be applied on IIR Filters**

Butterworth Analog Filter 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.

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**Filter that can be applied on IIR Filters**

Chebyshev Analog filter 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 stop-band.

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IIR/Realization

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High-Order IIR Filter 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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Errors in IIR Filters ADC quantizing noise, results from representing the samples of x(n) by small number of bits. Overflow errors, which result from arithmetic operations and save the output in a limited register length. 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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**Application in IIR Filters**

Telecommunication- in Transmitters as anti-aliasing filter. And, in Receivers anti-imaging filter. Digital Telephony-digital dual tone multi-frequency touch-tone receiver. Clock recover in Data communications.

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**References www.wikipedia.com**

Analog and digital signal processing by John Kronenburger and John Sebeson.

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THANK YOU

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IIR Filter design (cf. Shenoi, 2006) The transfer function of the IIR filter is given by Its frequency responses are (where w is the normalized frequency.

IIR Filter design (cf. Shenoi, 2006) The transfer function of the IIR filter is given by Its frequency responses are (where w is the normalized frequency.

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