Backup a SQLite database

I want to backup a single SQLite database daily up to 30 days back, but I also want to keep at least 2 backups at all times (i.e. if there have been no backups in the last 30 days because the database didn't change, I don't want to delete old backups).

I came up with this simple script that is supposed to run as a daily cronjob:

#!/bin/bash

BACKUP_FILE="/path/to/db.sqlite3"
BACKUP_DIR="$HOME/backups"

today=`date "+%Y-%m-%d"`

# Less than 31 days old, i.e. 30 days or younger
if find "$BACKUP_FILE" -type f -mtime -31 | grep -q .
then
        find "$BACKUP_DIR" -type f -mtime +30 -exec rm {} \;
fi

last_backup=$(ls -t "$BACKUP_DIR" | head -1)
if [ -n "$last_backup" ] && diff "$BACKUP_FILE" "$BACKUP_DIR/$(ls -t "$BACKUP_DIR" | head -1)" >/dev/null
then :
else
        cp "$BACKUP_FILE" "$BACKUP_DIR/$today.sqlite3"
fi

I'm not sure if using a nop in the second then clause makes sense, but it seemed cleaner to me than wrapping the condition in a test and checking $?.

The database is used by <20 people and not changed very often, but I'm not sure if I should lock the database anyways - and I'm also not sure how to lock it from a shell script.

Since this is the first bash script I've ever written for serious use, I'd appreciate any feedback on how it could be improved.

Don't use the obsolete syntax `...

Use the modern syntax $(...):

today=$(date "+%Y-%m-%d")

Simplify file deletion

Instead of deleting files with -exec rm {} \;, a simpler way is using -delete:

find "$BACKUP_DIR" -type f -mtime +30 -delete

Don't use the obsolete syntax head -N

head -1 is obsolete syntax. Use head -n 1 instead.

Don't repeat yourself

On these lines, $(ls -t "$BACKUP_DIR" | head -1) is repeated:

last_backup=$(ls -t "$BACKUP_DIR" | head -1)
if [ -n "$last_backup" ] && diff "$BACKUP_FILE" "$BACKUP_DIR/$(ls -t "$BACKUP_DIR" | head -1)" >/dev/null

The second use should be replaced with $last_backup.

Compare files using cmp

Instead of diff, it's more efficient to compare files using cmp:

if [ -n "$last_backup" ] && cmp -s "$BACKUP_FILE" "$BACKUP_DIR/$last_backup"

Avoid empty statements

Instead of the empty then clause of the final condition,
it's better to invert it (using DeMorgan's law):

if [ ! "$last_backup" ] || ! cmp -s "$BACKUP_FILE" "$BACKUP_DIR/$last_backup"
then
        cp "$BACKUP_FILE" "$BACKUP_DIR/$today.sqlite3"
fi

Delay operations until really needed

The today` variable is only used once at the end,
when certain conditions are fulfilled.
It would be better to create it right before it's needed.

StackExchange Code Review Q#153918, answer score: 2