  We present a detailed period analysis for 93 red semiregular variables by
means of Fourier and wavelet analyses of long-term visual observations carried
out by amateur astronomers. The results of this analysis yield insights into
the mode structure of semiregular variables and help to clarify the
relationship between them and Mira variables. After collecting all available
data from various international databases (AFOEV, VSOLJ, HAA/VSS and AAVSO) we
test the accuracy and reliability of data. We compare the averaged and
noise-filtered visual light curves with simultaneous photoelectric
V-measurements, the effect of the length versus the relatively low
signal-to-noise ratio is illustrated by period analysis of artificial data,
while binning effects are tested by comparing results of frequency analyses of
the unbinned and averaged light curves.
  The distribution of periods and period ratios is examined through the use of
the (log P_0, log P_1) and (log P_1, log P_0/P_1) plots. Three significant and
two less obvious sequences are present which could be explained as the direct
consequence of different pulsational modes. This hypothesis is supported by the
results for multiperiodic variables with three periods. Finally, these space
methods are illustrated by several interesting case studies that show the best
examples of different special phenomena such as long-term amplitude modulation,
amplitude decrease and mode switching.
