High Pass Filter with FIR (Window Methods) for Image Augmentation
High Pass Filter Design
Digital signal
processing (DSP) is a crucial part of modern electronics and communications
systems. To isolate or suppress specific frequency components of a signal,
filters are frequently employed in DSP. A high pass filter is a type of filter
that allows only high frequency sounds to pass through while weakening low
frequency vibrations. One way to create a high pass filter is to combine the
Window method with a Finite Impulse Response (FIR) filter. Since FIR filters
provide a linear phase response and consistent performance, they are frequently
utilized in DSP. In the window methods, the ideal filter response is multiplied
by a window function to create a finite length impulse response can then be
used to calculate the FIR filter’s coefficients.
High pass
filters with FIR are implemented using window methods in a variety of
applications, such as audio processing, image processing and biomedical signal
processing. They can be applied to signals to preserve their high-frequency
components while eliminating low-frequency noise and interference. The window
methods are widely utilized in DSP when developing FIR high pass filters. In
this approach, the required frequency response is multiplied by a window
function to get the filter coefficients. Secondly, the high pass filter will be
implemented using the MATALAB software. The task will entail choosing a
suitable window function and calculating the filter length in accordance with
the specified cutoff frequency. The amplitude response, phase response and
frequency response of the filter design will be analyzed and assessed.
The study will
also look into how different window functions and filter lengths affect the
accuracy of edge detection. In image processing and computer vision, edge
detection is a fundamental problem that includes locating the border of areas
of an image with various intensities or color values. The potential uses of
this technology in fields like robotics, surveillance, and medical imaging are
what give it its significance. High-pass filters are necessary for edge
detection, an important stage in image processing. The accuracy of object
detection and tracking can be increased using high-pass filters by enhancing
the quality of edges, which has significant implications in the scientific and
technical domains. For different image processing and computer vision
applications, high pass filters with FIR design and window methods can be
utilized to enhance or extract high-frequency edges from an image.
The objective of
this project is to create a high pass filter with FIR using window methods.
This project will cover the theory and methodologies of designing digital
filters, FIR filters, window methods and high pass filters. A suitable window
function will be selected during the design stage, and the MATLAB software will
be employed to generate the filter coefficients. The constructed filter will be
put to the test with various input signals, and its performance will be
evaluated using the filter’s parameters. Students will gain hands-on experience
in MATLAB based digital signal processing and filter design through the course
of this project. It will also clarify how high pass filters are actually
applied in real world settings.
Results
Edge detection
exists in multiple techniques using different approaches. In this paper, the
high-pass filter approach is used with FIR window techniques. The four (4) main
adopted windows are the rectangular, hanning, hamming and Blackman’s window.
It is important
to note that the input signal of this filter is an image. The image is
converted into grayscale to create a lower dimensional matrix (2D) which more
computable for edge detection purposes. By converting the image into grayscale
format, the color noise is reduced while the most important component only of
the image is contained. The frequency spectrum ranges from 0 to 255.
We see that the
input image signals create a spectral matrix. The weights of the matrix are
mostly below the 50% of 255 which is classified as low frequency shift within
that pixel weight range. However, as noticed in figure 1 above, some reflection
of light could be found on the side of the car which leads to higher pixel
weights. The frequency shift within this pixel weights creates a higher
frequency.
To use high-pass
filter in this context, it is expected that the lower frequencies shifts will
be attenuated creating an edge enhanced effect over the image.
Designing a
High-Pass filter using FIR windows
To design a
high-pass filter, some specifications is needed to constrain the filter
operations. Here, we create a sample calculation that may relay how high-pass
filter are designed using FIR windows.
To apply this
over the input image shown in figure 1, we first need to do further inspection
on the image frequency range.
Figure
2: frequency distribution
To understand how much we need to filter, we can plot the frequency distribution as shown in figure 2 above. The figure expresses the frequency components of the image showing how many pixels is bounded in that frequency.
Considering the
variable intensity of images, a sample calculation can be provided and will be
applicable for other images.
Figure
3: Magnitude and Phase response of rectangular window (order
10)
The figure above
plots the magnitude and phase response of the practical designed filter. It is
seen in the figure that the side lobes were down around -20dB with band-pass
approximately 300Hz and stop-band at approximately 200Hz.
Figure
4: Magnitude and Phase response of hanning window (order 10)
Expressed in
figure 4 above are responses with the side lobes down around -45dB with
band-pass extends to approximately 400Hz and stop-band at approximately 100Hz.
Here we can observe the growth of side lobe width. This may affect the ripple
response of the input signal with respect to the output signal.
Figure
5: Magnitude and Phase response of hamming window (order 10)
Shown in figure
5 above are responses with the side lobes down around -43dB with band-pass
extends to approximately 400Hz and stop-band at approximately 100Hz. Here we
can observe the growth of side lobe width. This may affect the ripple response
of the input signal with respect to the output signal.
Figure
6:Magnitude and Phase response of Blackman’s window (order 10)
The Blackman’s
window response shown in figure 6 above, expressed the reduced noise or ripple
from the effect of Blackman’s window. However, the window has a wider range of
frequency band at the main lobe. It is clearly seen in the above figure that
the band-pass extends to approximately 500Hz and stop-band at approximately
0Hz. Here we can observe the growth of side lobe width has been eliminated.
Roll off Rate
Figure
7: comparing roll-off rate at order 20dB
The above figures show the roll-off rate effectively changed when
the order is increased. The higher the order, the clear steepness can be seen
in the magnitude responses. As compared to the previous design, where the order
was set to 10, the roll-off rate was not very steep as could be witness on
these ones. Here, rectangular window is still the best as it quickly roll-off
to 200Hz or less. The hanning and hamming have similar effects where the
roll-off rates were a little bit improved as it drops close to 200 Hz. The
Blackman’s window has closed its main lobe width where it roll-off to
approximately 100Hz.
Therefore, for this application, the rectangular window may have executed the best in terms of roll-off rate and cut-off frequencies.
Applying Filter to Input Image
To apply the designed filter to the input image, the filter array is convolved with the image array resulting in a filtered image.
Figure
8: figure showing the filter effects over the input image at
10th order
The figure above
showed the resultant image after convolving the input image with the filter
matrix at 10th order. It can be seen that the rectangular window
shows a clear outline on the edges of the images in black lines. The hanning
and hamming window have slight differences but they both have white outlining
of the enhanced edges. However, the Blackman’s window shows slight of the
edges, but can be seen that it still attains some of the color components.
Figure
9: figure showing the filter effects over the input image at 20th
order
Figure 9 above
shows the edges enhancement by increasing the order to 20. The rectangular
window has slight added components while the hanning and the hamming windows
have extra details. The most impact goes to the Blackman’s window where the
color component from figure 10 disappeared resulting with a detailed edge
detector.
Histogram of Frequencies
The histogram of frequencies is
replotted to visualize the filtered frequency performed by the high-pass filter
in different window effects.
Figure
10: histogram of frequency at 10th order
Shown above are
the effect of the filters over the input image frequencies. It is seen that the
rectangular, hanning and hamming window attenuates the similar set of
frequencies while Blackman’s window still allows some frequencies as around 0.2
and 0.9Hz at normalized range.
Figure
11: histogram of frequencies at 20th order
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