## Chart: NMSE vs. Frequency ### Overview The image is a line chart showing the relationship between NMSE (Normalized Mean Squared Error) in dB and Frequency in Hz. There are four distinct data series represented by different colored lines: blue, orange, red, and brown. The chart illustrates how NMSE changes with frequency for each series. ### Components/Axes * **X-axis:** Frequency [Hz]. The scale ranges from approximately 30 Hz to 300 Hz. Major tick marks are present at 30, 40, 50, 60, 70, 80, 90, 100, 200, and 300 Hz. * **Y-axis:** NMSE (dB). The scale ranges from -25 dB to -5 dB. Major tick marks are present at -25, -20, -15, -10, and -5 dB. * **Data Series:** Four data series are plotted on the chart, each represented by a different color: blue, orange, red, and brown. There is no explicit legend, so the series are identified by color. ### Detailed Analysis * **Blue Line:** This line generally slopes upward, indicating that NMSE increases with frequency. * At 30 Hz, the NMSE is approximately -11.5 dB. * It dips to around -13 dB at 40 Hz. * It then rises sharply to approximately -7 dB at 100 Hz. * The line plateaus around -6 dB between 200 Hz and 300 Hz. * **Orange Line:** This line also slopes upward, showing an increase in NMSE with frequency. * At 30 Hz, the NMSE is approximately -20 dB. * It rises to approximately -11 dB at 100 Hz. * The line plateaus around -8 dB between 200 Hz and 300 Hz. * **Red Line:** This line shows a similar upward trend, with NMSE increasing with frequency. * At 30 Hz, the NMSE is approximately -23.5 dB. * It rises to approximately -14 dB at 100 Hz. * The line plateaus around -9 dB between 200 Hz and 300 Hz. * **Brown Line:** This line also slopes upward, indicating that NMSE increases with frequency. * At 30 Hz, the NMSE is approximately -25 dB. * It rises to approximately -15 dB at 100 Hz. * The line plateaus around -10 dB between 200 Hz and 300 Hz. ### Key Observations * All four data series show a general trend of increasing NMSE with increasing frequency. * The blue line consistently exhibits the highest NMSE values across the frequency range. * The brown line consistently exhibits the lowest NMSE values across the frequency range. * The NMSE values for all series tend to converge as the frequency increases beyond 200 Hz. ### Interpretation The chart suggests that, across the four data series, higher frequencies generally result in lower error (higher NMSE values, since the values are negative dB). The blue series performs the best (lowest error), while the brown series performs the worst (highest error). The convergence of the lines at higher frequencies indicates that the performance difference between the series diminishes as frequency increases. The initial dip in the blue line around 40 Hz is an anomaly that might warrant further investigation. The data demonstrates a clear relationship between frequency and NMSE, with performance generally improving at higher frequencies.

## Line Chart: NMSE vs. Frequency ### Overview The image presents a line chart illustrating the relationship between Frequency (in Hertz) and Normalized Mean Squared Error (NMSE) in decibels (dB). Four distinct data series are plotted, each represented by a different colored line. The chart appears to be evaluating the performance of a system or algorithm across a range of frequencies. ### Components/Axes * **X-axis:** Frequency [Hz], ranging from approximately 30 Hz to 300 Hz. Markers are present at 30, 40, 50, 60, 70, 80, 90, 100, 200, and 300 Hz. * **Y-axis:** NMSE (dB), ranging from approximately -25 dB to -5 dB. Markers are present at -5, -10, -15, -20, and -25 dB. * **Data Series:** Four lines, visually distinguishable by color: * Blue * Orange * Red * Dark Red/Brown ### Detailed Analysis Let's analyze each line individually, noting trends and approximate data points. * **Blue Line:** This line exhibits an upward sloping trend, starting at approximately -12 dB at 30 Hz and reaching approximately -4 dB at 300 Hz. It initially dips to around -14 dB at 40 Hz before steadily increasing. * **Orange Line:** This line also slopes upward, but starts at a lower NMSE value of approximately -20 dB at 30 Hz. It reaches approximately -6 dB at 300 Hz. It shows a more consistent upward trend than the blue line. * **Red Line:** This line begins at approximately -24 dB at 30 Hz and rises to approximately -10 dB at 300 Hz. It shows a relatively steep upward slope, particularly between 40 Hz and 100 Hz. * **Dark Red/Brown Line:** This line starts at approximately -25 dB at 30 Hz and increases to approximately -9 dB at 300 Hz. It has a similar upward trend to the red line, but consistently remains slightly below it. Here's a table summarizing approximate data points: | Frequency (Hz) | Blue Line (dB) | Orange Line (dB) | Red Line (dB) | Dark Red/Brown Line (dB) | |---|---|---|---|---| | 30 | -12 | -20 | -24 | -25 | | 40 | -14 | -16 | -18 | -19 | | 50 | -9 | -13 | -15 | -16 | | 60 | -7 | -11 | -13 | -14 | | 80 | -6 | -9 | -11 | -12 | | 100 | -5 | -8 | -10 | -10 | | 200 | -4 | -6 | -8 | -9 | | 300 | -4 | -6 | -10 | -9 | ### Key Observations * All four lines demonstrate a positive correlation between frequency and NMSE – as frequency increases, NMSE increases. * The dark red/brown line consistently exhibits the lowest performance (highest NMSE) at lower frequencies, but converges with the red line at higher frequencies. * The blue line consistently exhibits the best performance (lowest NMSE) across the entire frequency range. * The orange line falls between the blue and red lines in terms of performance. ### Interpretation The chart likely represents the performance of different noise reduction or signal processing algorithms across a range of frequencies. The NMSE metric indicates the error between the original signal and the processed signal. A lower NMSE value indicates better performance. The upward trend of all lines suggests that the algorithms become less effective at higher frequencies. The differences in performance between the lines indicate that some algorithms are more robust to frequency variations than others. The blue line's consistently lower NMSE suggests it is the most effective algorithm overall. The convergence of the red and dark red/brown lines at higher frequencies suggests that the performance difference between those algorithms diminishes as frequency increases. This could be due to limitations in the algorithms' ability to handle high-frequency components or due to the nature of the signal being processed. The data suggests that the choice of algorithm should be based on the frequency content of the signal. If the signal contains primarily low frequencies, the dark red/brown line algorithm might be sufficient. However, if the signal contains significant high-frequency components, the blue line algorithm would be the preferred choice.

## Line Graph: NMSE Performance Across Frequency Bands ### Overview The image depicts a line graph comparing the Normalized Mean Squared Error (NMSE) in decibels (dB) across a frequency range of 30–300 Hz for four distinct signals: an original signal and three filtered/noise variants. The y-axis represents NMSE (lower values indicate better performance), while the x-axis spans frequency in Hertz (Hz). Four colored lines (blue, orange, red, brown) represent different signal processing conditions. ### Components/Axes - **X-axis**: Frequency [Hz], labeled with markers at 30, 40, 50, 60, 70, 80, 90, 100, 200, and 300 Hz. - **Y-axis**: NMSE [dB], labeled with markers at -25, -20, -15, -10, -5 dB. - **Legend**: Positioned on the right, associating colors with labels: - Blue: "Original Signal" - Orange: "Filtered Signal 1" - Red: "Filtered Signal 2" - Brown: "Noise" ### Detailed Analysis 1. **Blue Line ("Original Signal")**: - Starts at ~-10 dB at 30 Hz, dips to ~-15 dB at 40 Hz, then rises to ~-5 dB by 300 Hz. - Shows a U-shaped trend with a minimum at 40 Hz. 2. **Orange Line ("Filtered Signal 1")**: - Begins at ~-20 dB at 30 Hz, peaks at ~-10 dB around 50 Hz, then stabilizes near ~-5 dB. - Exhibits a sharp upward trend between 30–50 Hz, followed by gradual improvement. 3. **Red Line ("Filtered Signal 2")**: - Starts at ~-25 dB at 30 Hz, rises to ~-15 dB by 100 Hz, then plateaus. - Demonstrates a steady improvement across the frequency range. 4. **Brown Line ("Noise")**: - Remains near ~-25 dB until 100 Hz, then increases to ~-15 dB by 300 Hz. - Shows minimal improvement, indicating poor performance. ### Key Observations - The "Original Signal" (blue) has the least improvement, with NMSE increasing at higher frequencies. - "Filtered Signal 1" (orange) achieves the best performance at mid-frequencies (~50 Hz) but degrades at extremes. - "Filtered Signal 2" (red) shows consistent improvement, outperforming the original signal at most frequencies. - The "Noise" line (brown) has the worst NMSE, confirming its role as a baseline for comparison. ### Interpretation The graph illustrates how signal processing techniques impact NMSE across frequencies. The original signal’s U-shaped trend suggests inherent frequency-dependent errors, possibly due to resonance or filtering artifacts. "Filtered Signal 1" improves NMSE significantly at mid-frequencies but introduces errors at extremes, indicating a trade-off in its design. "Filtered Signal 2" provides the most balanced improvement, suggesting it effectively mitigates errors across the spectrum. The "Noise" line serves as a control, highlighting the baseline degradation expected without processing. Notably, the divergence between the filtered signals and noise at 100 Hz implies that filtering becomes less effective at higher frequencies, potentially due to overlapping spectral components. The original signal’s dip at 40 Hz may reflect a specific frequency response characteristic, such as a resonant mode or a targeted filtering effect. This analysis underscores the importance of frequency-specific optimization in signal processing, with "Filtered Signal 2" emerging as the most robust solution for minimizing NMSE across the tested range.