Application of Modified Second-Order Frequency Transformations

International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395 -0056
Volume: 03 Issue: 02 | Feb-2016 www.irjet.net p-ISSN: 2395-0072
© 2016, IRJET | Impact Factor value: 4.45 | ISO 9001:2008 Certified Journal | Page 1522
APPLICATION OF MODIFIED SECOND-ORDER FREQUENCY
TRANSFORMATIONS
Karthika.M1, Sridevi.A2
1PG scholar, Department of ECE, SNS college of technology ,coimbatore , India,
2Associate professor, Department of ECE, SNS college of technology ,coimbatore , India
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Abstract - The frequency transformation based filters (FT
filters) give an complete control over the cutoff frequency. On
the other hand the cutoff frequency range of the FT filters is
inadequate. FTCDM filter has wider cut off frequency range
compared to the FT filter. But it also has limited range of
cutoff frequency range; To overcome the problem of limited
cutoff frequency range using a modified second-order
frequency transformation based filter (MSFT filter). The one-
to-one mapping condition stuck between the frequency
variables and use low-pass to high-pass transformationonthe
prototype filter to attain wider range of cutoff frequency. By
using the MSFT filter the cut off frequency range can be
improved.MSFT filter reduce the noise in noisy signal.MSFT
filter detect the original noiseless signal.
Key Words: Finite impulse response (FIR) filter,
frequency transformations, variable linear-phase
digital filter.
1. INTRODUCTION
variable finite impulse response (FIR) filters (FIR filters
whose frequency response can be changed on-the-fly, based
on the beloved specifications) are useful in wireless
communications, adaptive systems, audio signal processing,
and biomedical applications .In multistandard wireless
transportation variable filters are required for applications,
such as channelization (extraction of individual radio
channels from wideband input) and spectrum sensing.
Interoperability with the existing and future generation
wireless communications standards is thekeycharacteristic
of multi standard wireless mobile devices.
These devices should be able to support ultra-narrowband
as well as ultra-wideband frequencies. Therefore, the
channelizer in a multi standard radio should be able to
extract the channels of various bandwidths. (Channel
bandwidth specifications of various transportation
standards vary from 26 kHz to 23.1 MHz.) Due to its linear
phase property, FIR filter is regularly preferred to infinite
impulse response filter for the channelization task. Variable
FIR filters (filter whose passband width can be varied on-
the-fly) are required in these future generation wireless
communication devices.
A variable filter should have low area complexity so as to
satisfy the stringent area constraint for the handheld,
battery-operated terminals at the user end. It should also be
able to provide all the desired frequency responses more a
large frequency range, without the need of hardware
reimplementation. Designing such a variable filter with fine
control over the cutoff frequency and with low area
complexity is a challenging task, which is the objectiveof the
work presented in this paper. The frequency response of an
FIR filter can be changed by completely changing its
coefficients or by modifying the impulse response using
various operations.
In the case of programmable digital filters, the desired
frequency responses are obtained by updating all the filter
coefficients that can be stored in the memory. This is a very
effortless approach, and in general, such variable-coefficient
(or reloadable) filters are optimum in a sense that the filter
length for the particular frequencyresponsespecificationsis
minimum. However, when frequency response of a filter
needs to be changed frequently, the bulky number of
memory access operation would make updating routines of
these filters time-consuming. In addition, when the number
of frequency responses to be obtained is very large, huge
memory is required to store all the filter coefficients
corresponding to all the desired responses.
1.1 OBJECTIVE
Main objective is to increase the cut off frequency range and
reduces the noise in the required signal.
In the existing system the filter coefficientcanbefixed.In the
proposed system the coefficients can be generated by
different operations. When the frequency response of filter
can be changed frequently. Huge memory is required to
store all the filter coefficients.
Proposed MSFT filter has two significant changes compared
to the FT filter. First, apply the low-pass to high-pass
transformation to the prototype filter before applying the
second-order frequency transformation. Second, apply the
one-to-one mapping condition between the frequency
variables to obtain a two band response.

Fig-1: Normalized frequency
The response HL0 obtained from the MSFT filter & the cut
off frequency range is 0.35π
2. EXISTING SYSTEM
2.1 FIR FILTERS WITHPOWERS-OF-TWOCOEFFICIENTS
FIR filters with powers-of-twocoefficientsisgivenawaythat
the exponents of filter coefficients can be represent by the
canonical signed digit code with M ternary digits can be
selected from some subsets of {0,1,. . . , M-l}..
Implementation FIR filters with powers of-two
coefficients, which are often referredtoas2PFIR filters,have
received considerable attention in digital signal processing.
By employing only those coefficients that are sums and
differences of signed powers-of-two, each multiplication in
2PFIR filtering can be replaced with simple shift-and-add
operations. Implementation of a 2PFIR filter is particularly
efficient when its coefficients are fixed for dedicated
applications. The main disadvantage is coefficientsarefixed.
A newhardware-efficientarchitectureforprogrammable FIR
filters, are efficient high-speed filter architectures, much of
this work has focused on filters with fixed coefficients, such
as Canonical Signed Digit coefficient filter architectures,
multiplierless designs, or memory-based designs. In this
paper, we focus ondigit-serial,high-speedarchitectureswith
programmable coefficients. To achieve high performance
goals, we consider both of algorithm level and architecture
implementation level of FIR filters. In algorithm level, we
reformulate the FIR formulation in bit-level and take
the associative property of the addition in both the
digit-serial multiplications and filter formulations.
Variable finite impulse response (FIR) filters (FIR filters
whose frequency response can be changed on-the-fly, based
on the beloved specifications) are useful in wireless
communications, adaptive systems, audio signal
processing, and biomedical applications.
Fig -2.1: FIR filters with powers-of-two coefficients
2.2PROGRAMMABLE FIR FILTERS
Digital signal processing and advances in VLSI technologies
have had a great force on the application domains of
electronics. Amid the DSP applications, finite impulse
response (FIR) filters are important building blocks.
Recently, because of increasing demand for video signal
processing and transmission, high speed and high-order
programmable FIR filters have repeatedly been applied for
performing adaptive pulse shaping and signal equalization
on the received data in real time .F or this reason,an efficient
VLSI architecture for high-speed programmableFIRfiltersis
required. But, high-speed high-order programmable filters
are complicated to be implemented efficientlyforthereason
that of the high implementation cost and the
programmability requirements. The order of the filter is
given by the number of poles, which is another wayofsaying
the number of roots of the polynomial.

3. PROPOSED SYSTEM
The frequency response of an FIR filter can be altered by
completely changing its coefficients or by modifying the
impulse response using different operations. In the case of
programmable digital filters, the preferred frequency
responses are obtained by updating all the filter coefficients
that are stored in the memory. This is a very simpleadvance,
and in general, such variable-coefficient filters are optimum
in a sense that the filter length for the particular frequency
response requirements is minimum. When frequency
response of a filter needs to be changed frequently, the large
number of memory access operations would make updating
routines of thesefilterstime-consuming.Whenthenumberof
frequency responses to be obtained is very large, huge
memory is required to store all the filter coefficients
corresponding to all the desired responses.
Fig- 3:proposed MSFT Filter
In the proposed system design the variable filter each delay
of the filter structure is replaced by M delays to obtain a
multiband response and desired band is extracted using a
frequency masking filter. In the coefficient decimation
method , the impulse response of the fixedcoefficientfilteris
modified by retaining every Dth coefficient of the filter and
also replacing the lingering coefficients.Inthistechnique the
coefficient can be fixed by the range of frequency.
3.1 SECOND-ORDER FILTER DESIGN
Second Order Filters which are also referred to as VCVS
filters, because the op-amp is used as a Voltage Controlled
Voltage Source amplifier, are another important type of
active filter design because along with the active first order
RC filters looked at previously, higher order filter circuits
can be designed using them. First order filters can be easily
converted into second order filters simply by using an
additional RC network within the input or feedback path.
Define the second order filters as simply being, two 1st-
order filters cascaded together with amplification.
The second order filter has wider range of cut off frequency
range compare to the frequency transformation filter and
frequency transformation filter with combined co-efficient
technique. Second Order Filters which arealsoreferredtoas
VCVS filters, because the op-amp is used as a Voltage
Controlled Voltage Source amplifier, are another important
type of active filter design because along with the activefirst
order RC filters looked at previously, higher order filter
circuits can be designed using them. Firstorderfilterscan be
easily converted into second order filters simply by using an
additional RC network within the input or feedback path.
Fig-3.1:second order filter design

4. SIMULATION RESULT
Fig- 4: MSFT filter response
In that proposed system MSFT filter can increase the cut off
frequency range of 3.1 &1.23 compared to the existing
system the cut off frequency range can be increased.
5. CONCLUSION
The modifications to the second order frequency
transformation based filter to increase the cutoff frequency
range of low-pass filter responses.The second-order
frequency transformation and coefficient decimation based
filter (FTCDM filter) has wider compared totheFTfilter, but
the ratio of transition bandwidths of the transformed and
prototype filters is very high. The proposed modified
second-order frequency transformation based filter (MSFT
filter) has significantly wider cut off frequency range
compared to FT and FTCDM filters.
6. FUTURE WORK
The future work will be based on increasing the range of the
frequency transformation based filters. The frequency
transformation based filters range increased means
automatically obtain the low-pass responses over the entire
Nyquist band.
7. REFERENCES
[1]W.J.Oh,“Implementation of programmable
multiplierless FIR filters with powers-of-two
coefficients,” IEEE Trans. Circuits Syst. II, Analog
Digit. Signal Process., vol. 42, no. 8, pp. 553–556,Aug.
1995.
[2]T. Solla and O. Vainio, “Comparison of programmable
FIR filter architectures for low power,” in Proc. 28th
Eur. Solid-State Circuits Conf., Florence, Italy, Sep.
2002, pp. 759–762. K. H. Chen and T. D. Chiueh, “A
low-power digit-based reconfigurable FIR filter,”
IEEE Trans. Circuits Syst. II, Exp. Briefs, vol. 53, no.
8,pp. 617–621, Aug. 2006.
[3]R. Mahesh and A. P. Vinod, “Reconfigurablefrequency
response masking filters for software radio
channelization,” IEEE Trans. Circuits Syst. II, Exp.
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[4]R. Mahesh and A. P. Vinod, “Low complexity flexible
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[5]A.G.Constantinides, “Spectral transformations for
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pp. 1585–1590, Aug. 1970.
[6]S. J. Darak, A. P. Vinod, and E. M.-K. Lai, “A new
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[7]S. C. Chan, C. K. S. Pun, and K. L. Ho, “A new method
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Application of Modified Second-Order Frequency Transformations

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