# Reading Tapes Backwards: A Legitimate Approach to Saving Time and Money in Digitization Projects?
## 4 Results and Discussion  
After the digitization process, the audio files were analysed in order to verify whether, and in what circumstances, differences could be measured between the forward and backward reading of the same magnetic tape. Many metrics can be used to capture differences among signals (see, e.g., [30,31]), both in the time and frequency domains. In general, metrics in the frequency domain are considered more suitable for capturing differences in timbre nuances, or in wide-band noises. On the contrary, metrics in the time domain are more directly related to small local changes such as impulsive noises or transient responses. Given the electromechanical processes involved in the reading of a magnetic tape and the trivial observation that stationary signals are invariant to transformations along the time dimension, it is reasonable to expect that the main differences due to the reverse reading will be, if any, local changes, probably related to transient responses. On the basis of this assumption, we focused on a metric in the time domain and, in particular, the main feature assessed in the following analysis is the Euclidean distance between signals in the time domain. The Euclidean distance, however, cannot be directly used to compare the digital signals coming from the multiple readings. Indeed, it is well known that multiple readings of a tape using an analog recorder do not allow for a precise homogeneous alignment between the recordings, given the unavoidable and unpredictable mechanical effects while the tape is running. For example, as a result of these effects, the duration of a tape is slightly different each time it is read. This has led to a manual check of the audio samples and subsequent realignment in order to minimise the differences at the beginning of the tracks. Moreover, a Dynamic Time Warping algorithm was applied to guarantee a good alignment along the entire track. Secondly, the tracks were grouped in the same _block_, as impulses, drum, speech, and so forth, and were then divided between forward and backward readings. The Normalized Euclidean Distance (NED) for each audio frame was computed between two tracks within the same block in order to highlight the differences of the time signals. Afterwards, the NEDs obtained were labeled as congruent and non-congruent. The first refers to the comparisons between the forward or the backward readings (same directions); vice versa, the second refers to couples of opposite directions. The distribution of the data was analysed in order to ensure the requirements for ANOVA. Indeed, the Kolmogorov-Smirnov test highlighted that the data is non-normal, since it showed a natural limit shrinking to the left. Therefore, the power transformation \(\frac{\
u^{\lambda}-1}{\lambda}\), to ensure the Gaussian distribution of the data, was applied. A value of \(\lambda=\) 0.2 provided the necessary scaling factor. The first analysis of variance (ANOVA) showed a correlation between NED and the increasing value of the frame. In Figures 5 and 6, the boxplots of the first 100 of 233 frames of the audio files are shown for the congruent and non-congruent readings, respectively. It is possible to highlight the increasing value of the average NED according to the increasing number of frames. This result can be explained by the nature of an analog recorder, which is not able to provide a constant speed of tape reading. Indeed, the differences become more evident for longer readings than for shorter ones. Therefore, the dataset was reduced to the first 100 frames, since the analysis of variance showed a low correlation between NED and the frames, as shown in Table 1.  
Figure 5: Boxplot of first 100 frames’ NED of audio files for congruent readings. Figure 6: Boxplot of first 100 frames’ NED of audio files for non-congruent readings. Figures 7 and 8 show the boxplots for each block for the congruent and non-congruent comparisons, respectively. The most evident results are the differences of the average NED values that increase for the non-congruent comparisons.